Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative value.

Front

What is the parent function of absolute value functions?

Back

The parent function of absolute value functions is f(x) = |x|.

Front

How does the graph of f(x) = |x| transform when a constant is added or subtracted?

Back

Adding a constant shifts the graph vertically upwards, while subtracting a constant shifts it downwards.

Front

What effect does a negative sign in front of an absolute value function have on its graph?

Back

A negative sign reflects the graph of the absolute value function across the x-axis.

Front

What is the vertex of the absolute value function f(x) = |x - 3| + 2?

Back

The vertex is the point (3, 2).

Front

How do you determine the direction of the opening of an absolute value graph?

Back

If the coefficient of the absolute value expression is positive, the graph opens upwards; if negative, it opens downwards.

Front

What is the effect of multiplying an absolute value function by a constant greater than 1?

Back

Multiplying by a constant greater than 1 vertically stretches the graph away from the x-axis.

Front

What is the effect of multiplying an absolute value function by a constant between 0 and 1?

Back

Multiplying by a constant between 0 and 1 vertically compresses the graph towards the x-axis.

Front

How do you find the x-intercepts of an absolute value function?

Back

Set the absolute value expression equal to zero and solve for x.

Front

What is the equation of the graph that is a reflection of the parent function f(x) = |x|?

Back

The equation is f(x) = -|x|.