MTH 161 Ch1 Functions Graphs and Linear (1.3-1.5)

How do you tell if a graph is a function?

Vertical line test: if any vertical line hits the graph more than once, it is NOT a function.

How do you read domain and range from a graph?

Domain is the x-values read left to right. Range is the y-values read low to high.

Closed circle vs open circle in interval notation?

Closed circle means the value is included, so use a bracket. Open circle means excluded, so use a parenthesis.

What do arrows on a graph mean for domain or range?

The graph continues to infinity. Always use parentheses around infinity.

What does f(x) mean?

It is just another name for y. Function notation lets you be specific about which function and which input.

How do you evaluate f(3)?

Substitute 3 for every x and simplify.

How do you evaluate f(b+c)?

Replace every x with the whole expression (b+c), using parentheses, then simplify.

How do you solve f(x) = 7 algebraically?

Set the function equal to 7 and solve for x. A quadratic can give two solutions.

How do you find where f(x) = 3 on a graph?

Draw a horizontal line at y = 3 and read the x-values where it crosses the graph.

If S(t) = 9t - 4 is thousands infected after t days, what is S(4) and what does it mean?

S(4) = 32, which means 32,000 people infected after 4 days.

How do you find x-intercepts and y-intercepts?

x-intercept: set y = 0 and solve. y-intercept: set x = 0 and solve.

What is slope-intercept form?

y = mx + b, where m is the slope and b is the y-intercept.

Parallel vs perpendicular slopes?

Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals.

How do you factor x^2 + bx + c with the X-puzzle?

Find two numbers that multiply to c and add to b. Those numbers go in the two binomials.

Sign patterns when factoring trinomials?

Positive last term and positive middle: both numbers positive. Positive last term and negative middle: both negative. Negative last term: one positive and one negative, and the sign of the middle term tells you which is bigger.

Special products to memorize?

(a+b)^2 = a^2 + 2ab + b^2. (a-b)^2 = a^2 - 2ab + b^2. (a+b)(a-b) = a^2 - b^2.

Three laws of exponents?

Product: add exponents (x^a)(x^b) = x^(a+b). Quotient: subtract exponents. Power: multiply exponents (x^a)^b = x^(ab).

What are zeros of a function?

The x-values where the graph crosses the x-axis, also called x-intercepts, roots or solutions.