Construct and Analyze Piecewise Functions

Which graph shows a function with a range of all real numbers greater than or equal to -1?

Graph B

Which describes how to graph h(x) = -^3√x+8 by transforming the parent function?

Reflect the parent function over the x-axis, and translate it 8 units to the left.

Which table represents points on the graph of h(x) = ^3√-x+2 ?

Table C x| -6, 1, 2, 3, 10 y|2, 1, 0, -1, -2

What is the domain of the function f(x) = 3|x + 4| + 1?

all real numbers

What is the vertex of the graph of f(x) = |x + 3| + 7?

(-3, 7)

The graph of f(x) = |x| is transformed to g(x) = |x + 1| - 7. On which interval is the function decreasing?

(-∞, -1)

The function g(x) is defined as shown. (don't use the parenthesis. I didn't know how to do greater than or equal to signs.) g(x) = {3x-2, -4(</=) x<-2 {-x -1, -2(</=) x<1 {6, 1(</=) x (</=) 3 What is the value of g(0)?

-1

If g(x) = 2 − 1, what is g(−2.3)?

-7

Nina graphs the function y=⌊x⌋ to learn the properties of the parent floor function. What is the value of y when x=5.7?

5

The graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. Which statement about the domain and range of each function is correct?

The domain of the transformed function and the parent function are both all real numbers.

The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct?

The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.

The graph of g(x) is shown. Which statements describe the domain and range of g(x)? Select two options.

The maximum value of the range is 4. The range of g(x) is {y| -1 < y ≤ 4}.

Which statement best describes g(x) = ^3√x+6 -8 and the parent function f(x)= ^3√x ?

The ranges of g(x) and f(x) are the same, and their domains are also the same.

Which describes the range of the parent absolute value function?

{y|y >/= 0}

The graph shows a vertical translation of y = ^3√x. What is the range of the translated function?

{y|y is a real number}