Savvas 8th Topic 3 Mid-Topic Review

Topic 3 Mid-Topic Review

Replace this with a sub-header that can be in multiple lines. ​

• A relation is only a function if it passes the VLT or if the x's do not repeat.

​Function

• ANY set of points, table, graph, mapping, equation regardless of if it passes the VLT or if the x's repeat.

​Relation

Functions vs. Relations

What is a relation?

A relation is a set of inputs and outputs

• Ordered Pairs

• Table

• Graph

• Mapping Diagram

What is a Function?

A function is a relationship in which every input only has one output. In other words, when we are looking at a graph, table, points, diagrams etc. each x-value is assigned one y-value. Please watch this video for more clarification!

Multiple Choice

Which table represents y as a function of x?

• Table 1

• Table 2

Multiple Choice

Which relation represents y as a function of x?

• Mapping #1

• Mapping #2

Multiple Choice

Which graph does not represent y as a function of x?

• Graph #1

• Graph #2

Multiple Choice

Is the following a Function? Explain

(You may need to click on the picture to see it better)

• Yes; Each input has exactly one output.

• Yes; At least one input has more than one output.

• No; Each input has exactly one output.

• No; At least one input has more than one output.

Multiple Choice

Is the following a Function? Explain

• Yes; Each input has exactly one output. It passes the vertical line test.

• Yes; At least one input has more than one output. It fails the vertical line test.

• No; Each input has exactly one output. It passes the vertical line test.

• No; At least one input has more than one output. It fails the vertical line test.

Multiple Choice

Is the following a Function? Explain

• Yes; Each input has exactly one output.

• Yes; At least one input has more than one output.

• No; Each input has exactly one output.

• No; At least one input has more than one output.

Multiple Choice

Is the following a Function? Explain.

(2,5), (8, -2), (5,6), (9, -2)

• Yes; Each input has exactly one output.

• Yes; At least one input has more than one output.

• No; Each input has exactly one output.

• No; At least one input has more than one output.

Compare Linear and Nonlinear Functions

Comparing Constant Rate of Change

you can compare two linear functions by comparing their constant rate of change (their slope)

The picture is an example from your book.

Linear and Non linear Functions

• a non linear function (like the function for the area of an object) does not have a constant rate of change

• a linear function will have a constant rate of change

• for these questions you will be asked if the function is linear or not.

Multiple Choice

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts
• Ryan's Rafts

Multiple Choice

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Which service is cheaper for 8 movies in one month?

• Beth's service ($38 vs. $40) is cheaper
• Nate’s service ($42 vs. $44) is cheaper
• Nate’s service ($38 vs. $40) is cheaper
• Beth's service ($42 vs. $44) is cheaper

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Which function has the GREATEST rate of change?

Multiple Choice

What is the rate of change in the equation?
y=8x+6

• 8
• 6

Multiple Choice

What is the initial value in this equation?
y=8x+6

• 8
• 6