Math 4 Unit 2 Review

Math 4 Unit 2 Review

Piecewise, composition, and regessions

Piecewise functions

• Look at how many parts your piecewise function has

• Identify the parent function for each part

• Look for where (on the x-axis) graphs change

Multiple Choice

Match the graph with the correct equation.

Multiple Choice

How many pieces is this Piecewise Function composed of?

• 1
• 2
• 3
• 4

Multiple Choice

What are the domain restrictions for the green piece of this function?

• -2 < x ≤ 1
• -1 < x ≤ 0.5
• x > -2
• x ≤ 1

Multiple Choice

Which piecewise function corresponds to this graph? (Take your time)

• f(x) = { x  if x < 4;   -x+1  if x ≥ 4
• f(x) = { x  if x ≤ 4;  -x+1  if x > 4
• f(x) = { -x+1  if x < 4;  x  if x ≥ 4
• f(x) = { -x+1  if x ≤ 4;  x if x > 4

Multiple Choice

On the graph, which portion of the piecewise function is represented in red?

• x
• 0.5x + 2.5       
• -1
• 0.5x + 2

Composition

• Substitute one function for every x in the other function

• If finding at a value, substitute the number into the inside function first

• Using tables and graphs for composition at a value

Multiple Choice

• 3
• 1
• 4
• None of the Above

Multiple Choice

p(x) = 3x + 4
q(x) = 2x²
Find p(q(x))

• 10x²
• 18x² + 4
• 6x² + 4

Multiple Choice

p(x) = 3x + 4
q(x) = 2x²
Find p(p(-3))

• -9
• 7
• -11
• None of these

Regression Models

• Compare the r^2 values to help determine the best fit. The closer to 1, the better

• Compare residual plots to help. There should be no pattern.

• Remember in desmos to use the ~ instead of equals and include subscripts on x and y

Multiple Choice

• Linear

• Quadratic

• Exponential

• Square Root

Multiple Choice

Write the equation for the linear regression shown.

• $y=ax+b$

• $y=0.6x+0.1$

• $y=0.72x+r$

• $y=0.1x+0.6$

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 180 pages. 

• 12 chapters
• 15 chapters
• 18 chapters
• 21 chapters