Graphing Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input. It is defined as: f(x) = |x|, where |x| is the absolute value of x.

Front

What is the general form of an absolute value function?

Back

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

Front

How does the parameter 'a' affect the graph of an absolute value function?

Back

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

Front

What does the parameter 'b' do in the absolute value function?

Back

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

Front

What is the effect of the constant 'c' in the function f(x) = |x - c|?

Back

The constant 'c' shifts the graph horizontally. If c is positive, the graph shifts to the right; if c is negative, it shifts to the left.

Front

What does the constant 'd' do in the function f(x) = |x| + d?

Back

The constant 'd' shifts the graph vertically. If d is positive, the graph shifts upwards; if d is negative, it shifts downwards.

Front

How do you find the vertex of an absolute value function?

Back

The vertex of the function f(x) = a|bx + c| + d is located at the point (-c/b, d). This is the point where the graph changes direction.

Front

What is the vertex of the function f(x) = -|x - 1| - 2?

Back

The vertex is at the point (1, -2). This is where the graph reaches its maximum value.

Front

How do you graph the absolute value function f(x) = |x|?

Back

To graph f(x) = |x|, plot the vertex at (0,0) and draw two lines: one with a slope of 1 for x >= 0 and another with a slope of -1 for x < 0.

Front

What is the equation of the absolute value function that passes through the points (0, 2) and (2, 0)?

Back

The equation is f(x) = -|x - 1| + 2.