Topic 3.1-3.3 Linear Functions Review

Topic 3.1-3.3 Linear Functions Review

How this review works...

One slide will have a question and the next slide will go over the answer. If you get it correct, you can skip the review slide but if you get it wrong, read over the review to see what you did incorrectly.

Multiple Choice

What is the domain and range of the function?

• D: 3, 5, 7, 8, 11

  R: 6, 7, 7, 9, 14

• D: 6, 7, 7, 9, 14

  R: 3, 5, 7, 8, 11

• D: 3, 5, 7, 8, 11

  R: 6, 7, 9, 14

• D: 6, 7, 9, 14

  R: 3, 5, 7, 8, 11

Domain and Range

The DOMAIN is the list of x-coordinates and the RANGE is the list of y-coordinates (usually in numerical order) but you do NOT repeat any numbers if they appear more than once!

Multiple Choice

Is the mapping diagram a function? Explain why or why not.

• Yes; each input maps to one output

• Yes; one input maps to multiple outputs

• No; each input maps to one output

• No; one input maps to multiple outputs

Function or Not

To be a function, each INPUT must have only ONE OUTPUT. If an input has two or more different outputs, it can NOT be a function.

Multiple Choice

Is the graph a function? Explain why or why not.

• Yes; each input has one output

• Yes; one input has multiple outputs

• No; each input has one output

• No; one input has multiple outputs

Functions on the Coordinate Plane

When looking at a coordinate plane, you can use the vertical line test. This lines up the x-axis (INPUT) and shows how many times you touch a point on the graph (OUTPUT). If you intersect more than one point at a time, it fails and is NOT a function.

Multiple Choice

Danielle is filling up her gas tank with the $2.25 gas option. Her truck holds 27 gallons of gas and her total is $60.75.

What is a reasonable constraint on the domain of its situation?

• 0 < 2.25

• 0 < 27

• 0 < x < 27

• 0 < x < 60.75

Reasonable Domains

The domains are the INPUTS which are the x-axis on a coordinate plane. The inputs have to come first before you know the outputs...so you need to know how many gallons of gas she has filled up before you know the total cost. You CAN have a fraction of a gallon (CONTINUOUS) so all numbers between 0 and 27 make sense.

Fill in the Blanks

Function Notation

With function notation, you replace the y = with f(x) = which stands for "the function of x". When you see f(-3) it just means that the x is being replaced with -3. -1/3 (-3) = +1 and then add 13 to get 14.

Fill in the Blanks

Writing Linear Functions from Tables

First, you have to find the slope. If you can find the pattern between y and x ( y/x is slope) that is great but if not find the change in y's over the change in x's to find the slope.

Once you know the slope (m) use either slope-intercept form OR point-slope form to write the equation (solve for b).

Multiple Choice

For a basic subscription, a cable television provider charges an activation fee of $60, plus $125 per month.

Write a linear function represents the total cost of a basic cable subscription for t months?

What is the total cost for two years of service?

• y = 60 + 125t; $3,060

• f(t) = 60 + 125t; $3,060

• y = 125t + 60; $310

• f(t) = 125t + 60; $310

Writing a function using function notation

When asked to write a function, you MUST use f(x) and if they give you a variable besides x (like t) you must use that.

If the variable stands for months and the situation asks for years, you have to convert how many months are in that many years.

Multiple Choice

Describe how the graph of f(x) = 3x + 5 is transformed when given g(x) = f(x) + 12

• Shifted 12 units up

• Shifted 12 units left

• Vertical stretch by a factor of 12

• Horizontal compression by a factor of 12

Transformations

When you are ADDING it is a slide (translation) either UP (to the OUTPUT or to the f(x)) or LEFT (to the INPUT or the (x) only).

Multiple Choice

Describe how the graph of f(x) = 3x + 5 is transformed when given g(x) = f(4x)

• Shifted 4 units up

• Shifted 4 units right

• Vertical stretch by a factor of 4

• Horizontal compression by a factor of 4

Transformations using Multiplication

When you are MULTIPLYING to just the INPUT (or just the x) you have to think "sideways". A number > 1 would actually bring you closer to the y-axis so it is a Horizontal Compression and a number between 0 < x < 1 is a Horizontal Stretch.

Your y-intercept stays the same in this situation

Fill in the Blanks

Transformations that Rotate

When a function rotates it is being multiplied. If the line is steeper, it is a number greater than the original. Since the y-intercept changes, it is being multiplied by 3.

You can also see the change by writing out each equation in slope-intercept form and looking to see how many times larger the slopes are.

Transformations being rewritten into equations

Since the function h(x) = f(2x) has the INPUT being multiplied by 2 only, it would look like 2(2x) - 4 because only the INPUT is being doubled. Then solve and rewrite as a new function.

Poll

How ready do you feel for tomorrow's test?

• AWWW YEAH!!! BRING IT ON!!!

• Pretty solid! I think I got this!

• I am almost there...definitely studying tonight.

• Function? What? So confused...