~~~UNIT 1.1-1.2~~~

-CYU 1.1-

-4a. The Graph of a function y=f(x) is shown. Find f(-1)

f(-1) essentially means that the x of the f(x) {which is -1} is the X on the graph. So, we plot the point on -1 X. Because the equation is y=f(x), we know that the function must be on the Y-line. Thus, we draw a verticle line on the -1X point, and our value is where the line intersects with that line.

-5a. The complete Graph of a function y=f(x) is shown. The table shows some values for function f. Find the values to complete the table

We can find the missing values by plotting the inputs on the X line and seeing where the line intersects on the Y axis. One intersects with 1, 0 can only intersect with 0, and -2 intersects with 4.

-6a. The function N(t) gives the number of people in an auditorium, t hours after the doors open. Two hours after the doors open, there are 108 people in the auditorium.

Because N represents the number of people and T means time, N(t) represents the number of people after a specific time. Thus, the equation would be N(2)=108

-7abc. The table shows some values for the linear function f. Identify the y-intercept of the Graph of f. Determine the slope of the Graph of f. Write an equation for f(x).

a. To find the Y-intercept, we have to look for the input of 0. This is because the output from zero is the y-intercept on the 0,0 point. In the table, we see that 0’s production is 10. Thus, the Y-intercept is 10.

b. To determine the slope of the Graph, we have to use the slope formula x-x/y-y. For a table, we take the outer numbers on each side (The first and last) and use those as our points. That gives us an equation of 2—2/16-4. Both subtractions make a positive, and 16-4 is 12, so we get 4/12. Simplify to a slope of 1/3.

c. The equation will be y=mx+b. We already know the slope and y-intercept, so we plug them in for y=1/3X+10.

-10. Give the domain and range of P(d).

There are 30 days in June and 100% of the course to complete. Thus, the range and domain will be (0 X 30) and (0 X 100)

-Interval 1.1 Notation-

1. cd For a set of numbers shown on the number list below, represent the set using interval notation.

   Because the point is on an unclosed -4 and ends on a closed 11-point, the interval notation will be (-4, 11].

   -1.2 Quick Check-

2. b, state the minimum and maximum values of the function over its entire domain.

   The minimum and maximum points on the domain are the leftmost x point(minimum) and the rightmost x point(maximum). Thus, the minimum x point is (-8, -6), and the maximum x point is (9, 0).

   c. state the interval over which f(x)>0

   8 X 9

-1.2 More Practice-

4a. For the Function defined by f (x)=16-x^{2, Use} your calculator’s table option to help fill out the outputs in the table above.

Using the TBLSET function on the calculator would be best to get the table values. First, press the Y= button and type in the function on your calculator [(16-x²)]—press graph. Press the 2nd Graph to get the TABLE. Move the arrows to see all your points. Then press 2nd WINDOW to get TBLSET. Change the table’s settings to the number at which it starts on 1. Negative and Positive inputs of the same number have the same output.

6a. The Table below shows the temperature, in degrees Fahrenheit, as a function of the number of hours after 5:00 pm. What is the y-intercept of this function? What does it represent in the context of this problem?

The y-intercept is the output from the 0 input. Thus, the y-intercept is 68, according to the table presented. In the context of the problem, the y-intercept would represent the temperature. Since the Graph starts at 5 pm and goes from 5 pm, the y-intercept would be the temperature at or after 5 pm.

Quiz Review:

-4c. The problem claims that the postcard’s relationship has w(l) = the width of the postcard multiplied by the length since that’s how we calculate our width. The l remains long, so to get our formula (since we know l*w=A), we would use the formula Area=l*w(l).

-5b. Since x=the x in f(x), we would plug -1 into the f(x) formula. (-1-3)²-2= 14. We can find what g(0) is since the formula for g is y=g(x), meaning that the Y value on the listed X value point is our number. Following the Graph, this makes g(0) -2. Thus, when we subtract f(x) {14} from g(0) {-2}, we get a final answer of 12.

-6ab. To get f(x)+g(x), we add the functions together because the problem claims that f(x) and g(x) equal their respective functions. Simplify 2(x-1) by distributing to get 5x-2+2x-2. Then, we combine the common factors to get a simplified answer of 7x-4.

To get f(x)-g(x), we do the same thing as above, subtracting from each other rather than adding. 5x-2-2x-2. 7x-4=3x, our answer.

-8. When we only have one poiInfinitynfinity, we use X>/<(depending on where the segment is going) other points on the line. When using interval, notInfinitynfinity uses (), not [].

-10. When using interval, notInfinitynfinity uses (), not []. Infinity also uses </>; other points are not classified as open circles or infinite use ≤/≥. The increasing intervals are from below 0 to 0, so we keep it with those points. The same applies to increasing intervals; we use interval notation to mark this, not inequalities.

-11a. Plug 4 in for X since the function is f(4). Absolute value lines don’t mean anything different; they make everything negative regardless.

-12ab. Because the function is f(x), a+c can be plugged in for X. Thus, 2a-4(a+c)can be distributed to 2a-4a+4c. Simplify and combine to get -2a+4c.

Plug the 6a-3b in for x since the function is h(x). -3(6a-3b). Distribute and simplify to get a final answer of -18a+9b.

15cde. Because we don’t have a direct function line, we must list all the points for the domain and range.

19f. Because there are multiple points on this line, we have to have the domain for each one.

-Quiz 1.1-1.2-

-1a. State the Domain and Range of the Graph.

-2a.c. A function where f= y=f(x) is shown on the graph. Evaluate f(4). Determine the intervals where f(x) is increasing.

-3d.g. Given the function f(x) on the graph, state the y-intercept of f(x). Over the interval (-∞, -10), is the function increasing or decreasing?

~~~UNIT 1.3-1.5~~~

Ask about converting standard form into slope-intercept form

-CYU 1.3-

2. Find the average rate of change of f(x)=3x-8 between x=-7 and x=4.

Because x=-7 and x=4, we plug both X’s in our equation to get corresponding Y-POINTS. Remember , B=Y-Intercept, Y=Y points. When both X’s are plugged in, we get corresponding Y points of -29 and 4. Use the slope formula to get the average rate of change. Remember, -7 and 4 are your X points.

6b. Find a possible value for the number of people in line at t=6, given that the average rate of change of P between t=3 and t=6 is negative, but the average rate of change between t=5 and t=6 is positive.

9. The graph of y=g(x) is shown. Order the following from least to g

Calculate the slope between each point on the given intervals for each problem using rise over run from each point on the given X intercept in the inequalities. Remember when slopes are harmful, and 2 negative numbers on a slope instead make an upbeat version of that slope. Order them from least to greatest. Using this formula, the order is III, II, IV, I.

-CYU 1.5-

4. Fill in the blanks to write a piecewise equation.

   If you buy 2 pounds or less, then the price is 9.95. If you buy more than 2 pounds, you pay 7.95. We already have the inequality laid out for us, so we know that the equation will be C(p)= 2 equations because there are 2 possible outcomes. The first is 9.95 if you pay 2 pounds or less. So, our equation will be 9.95 if 0<p≤2. This is because to pay 9.95, you must buy somewhere between 0 and 2 pounds. For the 2nd equation, it is 7.95 for over 2 pounds. So, our equation will be 7.95 if p>2. Put both into the complete function equation of C(p)= 9.95 0<p≤2, 7.95 p>2.

6. Graph y=f(x)

8bc. Does the club charge a higher hourly rate with 2 children than 1? If a family has more than two children, how much does the club additionally charge per hour?

The club does not charge a higher rate. This is because the shown function inequality uses ≤2, which means less than or equal to 2 regarding the first price. Thus, the number for 2 or 1 child is the same. The club additionally charges $4 an hour for more than 2 kids. The function shows an equation for 10 +4(x-2). X is equal to the number of children. Because we are asking for per child, we are essentially asking for the average rate of additional charge, where we can look at the slope in the equation, which is 4. Remember that asking for something usually refers to the average rate of change.

Point Slope Review. Graph the line y+4=-5/2(x+3) on the coordinate plane.

The function line tells us that the line has a point of (3, 4) by giving us those numbers on the y and x point segments of the equation. The line also gives us the slope (-5/2), so use rise over run with the slope from the point (3, 4) across the entire graph to get your line.

-Mastery Check 1.3-

Always look for the side of the table with both numbers as X-intercepts. Find the corresponding Y-intercept by looking at each number’s corresponding point on the other side of the table. Use the slope formula to get the average rate of change.

Solution (1/4).

To get the average rate of change, we have to have both X points and both Y points, we know the X points are the numbers on the inequality, so we know the x points are 0-8. To get the Y points, plug in each X into the equation separate times to get the corralatting y outcome for the X. This gets us points of 18-10. Use slope form rise/run to get slope/average rate of change.

Solution (-1).

We know from the inequality the X points are 4 and 5. To get the Y points, find the points on the graph that is on each X points. Look and see what their corralating y points are. These are your y points. Use rise/run slope form to get average rate of change.

Solution(-4).

Plot a point at -7 y. Because slope is -x(-1) go down 1 and right 1. This is your line. Draw it across the entire graph. Because the inequality is -6≤x<-1, the line is only true between the x points of -6 and -1; so erase the rest of your line except for the space between that. Fill in circles as needed. The second line, place a point on y -5. Slope is 1, so go up and right 1. This is your line. Draw it across the entire graph. Because the line is only true between -1 and 4, erase your line except for those in between spaces. Fill in circles as needed.

Stopped here

Solution (3). Use parentheses when using a double negative. Aka -6=x -x² —→ -(-6)²

Solution (-3) Use Parentheses when using a double negative. Aka -6=x -x² —→ -(-6)²

^{-CYU 1.4-}

2. A table of selected values is given for odd function X. Find 3 other ordered pairs.

   8. Benedickt was asked to determine if the function f(x)=x³-4^×2-4x+19

   9. Determine if the statement is true or false. Reflecting an even or odd function across the x-axis does not affect its function’s symmetry.

      -Mastery Check 1.5-

      Solution: 2

      
      

      HOW TO GRAPH PIECEWISE FUNCTIONS:

      Take the equation above as an example. The -1 is the y-intercept, so we’ll place a point there. Because there is no x, we have no slope, so we keep it a straight line across the ENTIRE graph. Then, look at your inequality. Because the inequality states -4<x<1, this means the line is only valid between those X points. Erase the rest of the graph and fill in circles as needed. Because the second one has an equation of x+2, we will plot a point of 2 on the y-intercept, then, because X is placed before 2, we know X (which is equal to 1/1) is our slope; so we will graph a line using that slope from the y-intercept across the ENTIRE graph. Plot the line in regards to the inequality and fill in circles as needed.

      HOW TO EVALUATE PIECEWISE FUNCTIONS:

      Take the above equation as an example. Find f(1). Find the X point for 1 on the graph. Then, look on the Y-line for the corresponding point. If there are multiple points, choose the one with a closed circle. It is undefined if no closed circle lines exist on the following Y-intercept.

      ~~ALGEBRA 1 REVIEW~~

      -CYU A-

      1a. Rewrite the equation in slope-intercept form: x+2y=-2

      2. Write an equation in a point-slope form that passes through the points (-3,8) and (5,-4).

      3. Write an equation in slope-intercept form that goes through the points (3, -4) and (-3, 5)

      4. Write an equation in a standard form that passes through the points (6, -4) and (12, 2)

      -CYU B-

      2. Which of the following points passes through the point (-4, -8)?

         6a. The points (-3, 6) and (6, 0) are plotted on the grid below. Find an equation, in y=mx+b form, for the line passing through these two points.