Praxis Math 2

What is a function?,A relation where each input (x) has exactly one output (y).

What is the domain of a function?,The set of all possible x-values (inputs).

What is the range of a function?,The set of all possible y-values (outputs).

What test determines if a graph is a function?,The vertical line test.

Vertical line test definition,If a vertical line touches a graph more than once the relation is not a function.

What is function notation?,A way of writing functions using f(x) to represent the output.

Example of evaluating a function,If f(x)=2x+3 then f(4)=11.

What is a relation?,A set of ordered pairs (x,y).

Ordered pair meaning,The first number is x (input) and the second number is y (output).

What makes a relation NOT a function?,One input has more than one output.

What is a rational function?,A function that is a ratio of two polynomials.

Vertical asymptote rule,Set the denominator equal to zero.

What is a vertical asymptote?,A vertical line the graph approaches but never touches.

Horizontal asymptote rule (same degree),Divide leading coefficients of numerator and denominator.

Horizontal asymptote meaning,A horizontal line the graph approaches as x becomes very large.

x-intercept rule for rational functions,Set the numerator equal to zero.

y-intercept rule,Substitute x = 0.

What is an asymptote?,A line the graph approaches but does not reach.

What is a polynomial?,An expression made of variables and exponents added or subtracted.

What is a logarithm?,The exponent needed to produce a number.

Common logarithm definition,Log base 10.

Log product rule,log(a)+log(b)=log(ab).

Log quotient rule,log(a)-log(b)=log(a/b).

Log power rule,log(a^b)=b log(a).

Log to exponential conversion,log_b(x)=y means b^y=x.

What does log(100)=2 mean?,10^2=100.

What is log(1000)?,3.

What is an exponent?,A number that tells how many times a base is multiplied.

Exponent rule for multiplication,a^m * a^n = a^(m+n).

Exponent rule for division,a^m / a^n = a^(m-n).

Power of a power rule,(a^m)^n = a^(mn).

Zero exponent rule,a^0 = 1 (for a ≠ 0).

Negative exponent rule,a^-n = 1/a^n.

What is solving an equation?,Finding the value of a variable that makes the equation true.

What is factoring?,Writing an expression as a product of simpler expressions.

What is distributing?,Multiplying a number across terms inside parentheses.

Slope formula,(y2 - y1)/(x2 - x1).

Slope meaning,Rate of change of a line.

Slope-intercept form,y = mx + b.

What is m in slope-intercept form?,Slope.

What is b in slope-intercept form?,Y-intercept.

Triangle area formula,1/2 × base × height.

Rectangle area formula,length × width.

Circle area formula,πr².

Circle circumference formula,2πr.

Pythagorean theorem,a² + b² = c².

Hypotenuse definition,The longest side of a right triangle.

Mean definition,Average of numbers.

Mean formula,Sum of values divided by number of values.

Median definition,The middle number when data is ordered.

Mode definition,The number that appears most often.

Range in statistics,Largest value minus smallest value.

Probability formula,Number of favorable outcomes divided by total outcomes.

Probability range,Between 0 and 1.

Probability of impossible event,0.

Probability of certain event,1.

What is a ratio?,A comparison of two quantities using division.

What is a proportion?,Two ratios set equal to each other.

What is a system of equations?,Two or more equations solved together.

Solution to a system,A point that satisfies both equations.

What is a quadratic equation?,An equation with the highest power of x equal to 2.

Standard quadratic form,ax² + bx + c = 0.

Difference of squares formula,a² − b² = (a + b)(a − b).

Perfect square trinomial,a² + 2ab + b² = (a + b)².

What is a coordinate plane?,A grid formed by the x-axis and y-axis.

Origin definition,The point (0,0) where the axes intersect.