Absolute Value Functions

Front

What is 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 output.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where a, b, c, and d are constants.

Front

What does the 'a' in the absolute value function f(x) = a|bx + c| + d represent?

Back

The 'a' represents the vertical stretch or compression and the direction of the graph. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

What does the 'b' in the absolute value function f(x) = a|bx + c| + d represent?

Back

The 'b' represents the horizontal stretch or compression. If |b| > 1, the graph is compressed; if |b| < 1, it is stretched.

Front

What does the 'c' in the absolute value function f(x) = a|bx + c| + d represent?

Back

The 'c' represents the horizontal shift of the graph. If 'c' is positive, the graph shifts left; if negative, it shifts right.

Front

What does the 'd' in the absolute value function f(x) = a|bx + c| + d represent?

Back

The 'd' represents the vertical shift of the graph. If 'd' is positive, the graph shifts up; if negative, it shifts down.

Front

What is the vertex of the absolute value function f(x) = a|bx + c| + d?

Back

The vertex is the point ( -c/b, d ), which is the highest or lowest point of the graph depending on the value of 'a'.

Front

What is the line of symmetry for the absolute value function f(x) = a|bx + c| + d?

Back

The line of symmetry is the vertical line x = -c/b.

Front

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

Back

To find the x-intercepts, set f(x) = 0 and solve for x.

Front

What is the effect of a negative 'a' value on the graph of an absolute value function?

Back

A negative 'a' value reflects the graph across the x-axis, making it open downwards.