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 and the direction 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 parameter 'c' in the function f(x) = |x + c|?

Back

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

Front

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

Back

The parameter 'd' shifts the graph vertically. If 'd' is positive, the graph shifts up; if 'd' is negative, it shifts down.

Front

What is the vertex of the absolute value function f(x) = |x|?

Back

The vertex of the function f(x) = |x| is at the point (0, 0). It is the lowest point of the graph.

Front

How do you graph the function f(x) = |x - 2|?

Back

To graph f(x) = |x - 2|, plot the vertex at (2, 0) and create a V-shape opening upwards.

Front

What is the equation of the graph that opens downwards with vertex (3, 5)?

Back

The equation is f(x) = -|x - 3| + 5.

Front

How do you determine the y-intercept of the function f(x) = |x| + 2?

Back

To find the y-intercept, set x = 0. Thus, f(0) = |0| + 2 = 2, so the y-intercept is (0, 2).