The piece-wise linear functions can be written as follows:
.
.
.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:
.
For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:
.
For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:
m = (-3 - (-5))(3 - 2) = 2.
The rule is:
y = 2x + b.
When x = 2, y = -5, hence:
-5 = 2(2) + b
b = -9.
Hence:
.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
Z = 2
Step-by-step explanation:
This tape diagram is split into two equal parts.
Since 2 and 2 are equal, and since 2 and 2 have a sum of 4, then z is equal to 2.
Very simple.
Let's say you have an equation.
f(x) = x^2
You are asked to find the value for y when x equals 1.
The new equation is: f(1) = (1)^2
f(1) = 1
When x = 1, y = 1.
The same concept is applied here.
In the graph, where does x equal 0?
It equals zero at the origin.
Is there any y-value associated with 0?
Yes, there is.
Y equals five when x equals 0.
So
h(0) = 5
Answer: Choice #3 - compressed horizontally and translated by 4 units to the right.

This corresponds to horizontal shift to the right by 4 units and a horizontal compression.