10.7 Comparing Functions

Title: 10.7 Modeling and Curve Fitting

EQ: How can you tell from a table if the data is linear? exponential? or quadratic?

Put your graphing HW worksheet on your desk

Key Structures: Linear

Multiple Choice

Where is the y-intercept in this graph?

• (0,2)

• (4,0)

Multiple Choice

Where is the x-intercept in this graph?

• (0,2)

• (4,0)

Key Features: Absolute Value

• Vertex (corner point): where the graph turns from decreasing to increasing

• Axis of Symmetry: an invisible line that cuts the graph into two equal halves through the vertex

Multiple Choice

Where is the vertex of this graph?

• (0,3)

• (3,0)

Multiple Choice

Where is the axis of symmetry of this graph?

• x = 3

• x = 0

Exponential Functions (y=a(b)^x)

• a: y-intercept (where the curve crosses the y-axis or the y-value when x=0)

• b: growth or decay factor (what is being multiplied or divided when you look at the y-values)

• Growth if b>1

• Decay if b is between 0 and 1

Quadratic Functions

Open Ended

Compare the linear function to the Quadratic - what do you notice about the x-intercepts?

Open Ended

Compare the Linear Absolute Value Function to the Quadratic Function. What key feature(s) do they share?

Multiple Choice

Identify the following function. 

• Linear

• Exponential

• Quadratic

• Neither

Multiple Choice

Identify the following function. 

• Linear

• Exponential

• Quadratic

• Neither

Multiple Choice

Is the equation linear, exponential or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Pick a function that best models the following situation:  A babysitter getting paid hourly.

• Exponential

• Linear

• Quadratic

• Neither

Multiple Choice

Pick a function that best models the following situation:  The altitude of a bumblebee going to land on a flower.

• Exponential

• Linear

• Quadratic

• Neither

Multiple Choice

Is the equation linear, exponential or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Pick a function that best models the following situation: A speed of a rollercoaster from start to finish. 

• Exponential

• Linear

• Quadratic

• Neither

Characteristics of Functions: From looking at a table

• Linear Functions have a constant rate of change - Add/Sub the first set of y values.

• Quadratic Functions - Second difference is equal

• Exponential Functions - Common ratio - you can multiply or divide to get to the next y value

​Is it Linear or Exponential?

​When given a table, look for a common difference or a common ratio.

​- If the pattern is add/subtract, the function is linear.

​- If the pattern is multiply/divide, the function is exponential.

​Examples:

Since the pattern is adding, the function is linear.

Since the pattern is multiplying, the function is exponential.

Multiple Choice

Is the pattern adding/subtracting or multiplying/dividing?

• adding/subtracting

• multiplying/dividing

Multiple Choice

Is the function linear or exponential?

• linear

• exponential

Multiple Choice

What is the y-intercept?

• 1/3

• 1

• 3

• 9

Multiple Choice

What function best models the data in the table?

• linear

• exponential

• quadratic

Multiple Choice

Which student's number pattern is linear?

• Ashley

• Hector

• Jamal

• Karina

​Writing the "rule" or equation

​Once we now what the "a" and "b" values are, we can write the equation that represents the function.

​For Example:

​We found earlier that

a = 8

b = 2

​- We use the template: y = a(b)^x

​y = 8(2)^x

Multiple Choice

Given the table, determine the equation of the function. 

• y = 4(4)^x

• y = 4(¼)^x

• y = 4(x-0)² + 4

• y = 2(x-1)² + 16

Multiple Choice

Given the table, determine the equation of the function. 

• y = 4x + 1

• y = 1x + 4

• y = -4x + 1

• y = -1x + 4

Multiple Choice

Given the table, determine the equation of the function. 

• y = 2(½)^x

• y = 2x + 3

• y = -3x + 2

• y = 3(2)^x

Multiple Choice

Is the pattern adding/subtracting or multiplying/dividing?

• adding/subtracting

• multiplying/dividing

Multiple Choice

What is the y-intercept?

• 1/2

• 2

• 4

• 8

Multiple Choice

What is the equation that models the data in the table?

• $$y=2^x$$  

• $$y=2\left(2\right)^x$$  

• $$y=4\left(2\right)^x$$  

• $$y=2\left(4\right)^x$$  

Multiple Choice

What is the equation that models the data in the table?

• $$y=2\left(\frac{1}{2}\right)^x$$  

• $$y=\left(\frac{1}{2}\right)^x$$  

• $$y=\left(\frac{1}{3}\right)^x$$  

• $$y=\left(\frac{1}{4}\right)^x$$  

Multiple Choice

Give the equation for the graph

• y = 5x - 3

• y = 4x + 2

• y =-2x + 5

• y = - 2x + 4

Multiple Choice

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

Multiple Choice

What type of function does this equation represent? $$Y=4\left(\frac{1}{2}\right)^x$$  

• Linear Function

• Quadratic Function 

• Exponential Function

• Not a Function

Multiple Choice

Which student represents a Quadratic Function?

• Beth

• Maria

• Tracy

• None of the above

Multiple Choice

Which student represents an Exponential Function?

• Beth

• Maria

• Tracy

• None of the above

Multiple Choice

All Linear Functions have a __________________.

• Common Difference

• Common Ratio

• Difference of Differences

• There's no way to tell

Multiple Choice

All Exponential Functions have a ________________.

• Common Ratio

• Common Difference

• Difference of Differences

• None of these

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 relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.

• Yes, because each x-value has only one y-value paired with it.

• No, because the x-value 11 has two y-values pair with it.

• No, because each x-value has only one y-value paired with it.

Multiple Choice

Which of the following is not a function?

Multiple Choice

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

• 8

• 6

10.7 HW Pg 235 #8-14 EVEN, Pg 236 #17-19

We will be taking a quiz 4/18 and 4/19

All Ch. 10 HW is due by then

You have only had 18 TOTAL problems, so there should be no reason to have missing Ch. 10 HW