Absolute value functions and graphs

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

• It shifts the graph vertically.

• It shifts the graph horizontally.

• It reflects the graph across the x-axis.

• It stretches the graph horizontally.

How do you determine the vertex of the function f(x) = a|x - h| + k?

• The vertex is at the point (h, k), where h is the horizontal shift and k is the vertical shift.

• The vertex is at the point (0, 0) regardless of the values of a, h, and k.

• The vertex is at the point (h, 0) where h is the horizontal shift.

• The vertex is at the point (k, 0) where k is the vertical shift.

What is the effect of a vertical shrink on the graph of an absolute value function?

• A vertical shrink by a factor of a (0 < a < 1) makes the graph wider.

• A vertical shrink by a factor of a (0 < a < 1) makes the graph taller.

• A vertical shrink by a factor of a (0 < a < 1) has no effect on the graph.

• A vertical shrink by a factor of a (0 < a < 1) flips the graph upside down.

How does the graph of f(x) = -|x| + 1 differ from f(x) = |x|?

• The graph of f(x) = -|x| + 1 is reflected across the x-axis and shifted up by 1 unit.

• The graph of f(x) = -|x| + 1 is reflected across the y-axis and shifted down by 1 unit.

• The graph of f(x) = -|x| + 1 is identical to f(x) = |x|.

• The graph of f(x) = -|x| + 1 is shifted down by 1 unit without reflection.

How do you find the x-intercepts of the function f(x) = |x| - 5?

• Set the equation |x| - 5 = 0, which gives x = 5 and x = -5 as the x-intercepts.

• Set the equation |x| + 5 = 0, which gives x = 5 as the only x-intercept.

• Set the equation |x| - 5 = 0, which gives x = 0 as the only x-intercept.

• Set the equation |x| - 5 = 0, which gives x = 10 and x = -10 as the x-intercepts.

What is the significance of the vertex in an absolute value function?

• It is the point where the function changes direction and is the minimum or maximum point of the graph.

• It represents the x-intercept of the function.

• It indicates the slope of the function at any given point.

• It is the point where the function is undefined.

What effect does multiplying the absolute value function by a negative number have?

• It shifts the graph to the right.

• It reflects the graph across the x-axis.

• It stretches the graph vertically.

• It compresses the graph horizontally.

What is the domain and range of the absolute value function f(x) = |x|?

• Domain: all real numbers (-inf, inf); Range: all non-negative numbers [0, inf)

• Domain: all real numbers (-inf, inf); Range: all real numbers (-inf, inf)

• Domain: all non-negative numbers [0, inf); Range: all real numbers (-inf, inf)

• Domain: all real numbers (-inf, inf); Range: all negative numbers (-inf, 0)

What is the absolute value of a number?

• The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

• The absolute value of a number is the number itself if it is positive, and zero if it is negative.

• The absolute value of a number is the square of the number.

• The absolute value of a number is the opposite of the number.

What is the parent function of absolute value?

• f(x) = x^2

• f(x) = |x|

• f(x) = x + 1

• f(x) = sin(x)