Math 3: EOC Review Unit 1 - Function Basics

Front

What is the RANGE of a function?

Back

The RANGE of a function is the set of all possible output values (y-values) that the function can produce. For example, the range of the function f(x) = x^2 is [0, ∞) because the output is always non-negative.

Front

How do you find the difference of two functions f(x) and g(x)?

Back

To find the difference of two functions, you subtract the second function from the first: f(x) - g(x). For example, if f(x) = 6x - 8 and g(x) = -3x + 2, then f(x) - g(x) = (6x - 8) - (-3x + 2) = 9x - 10.

Front

What does f(-3) represent in a function?

Back

f(-3) represents the output of the function f when the input is -3. It is the value of the function at x = -3.

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^(-1)(y) takes y and produces the original input x.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function, swap the x and y variables and solve for y. For example, for f(x) = -4x - 12, swap to get x = -4y - 12, then solve for y to find the inverse.

Front

What is the domain of a function?

Back

The DOMAIN of a function is the set of all possible input values (x-values) that the function can accept. For example, the domain of f(x) = 1/x is all real numbers except x = 0.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the input into the function's equation. For example, to evaluate f(x) = 2x + 3 at x = 4, calculate f(4) = 2(4) + 3 = 11.

Front

What is a vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.