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

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.