What Happened to the Equation?

Unit 5 ● Lesson 2 ● Activity 1

Graph each function using technology. Describe how to transform f(x) = to get to the functions shown here in terms of both the graph and the equation.

​

g(x) =

h(x) =

​

​

​

​

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Warm-up

Moving Functions

​

​

Unit 5

Lesson 2

Transformations of Functions

Expressions and Equations

​

​

ALGEBRA 2

Unit 5 ● Lesson 2

I can use function notation to represent a vertical or horizontal translation from one graph to another.

Learning

Targets

Algebra 2

Shift it!

Use technology (desmos or calculator) to graph the parent function

f(x) = x²

Now graph each of the following functions and describe the result:

​

1. f(x) + 3

​

• f(x) - 3

​

• f(x + 3)

​

• f(x - 3)

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Translations

A translation (slide) moves a figure up, down, left or right.

• When a constant is added or subtracted from the parent function, this translates the graph up(added) or down(subtracted)
• When a constant is added or subtracted from x before evaluating a parent function, this translates the graph left(added) or right(subtracted)

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Glossary

Predict it!

Predict what will happen to the parent graph with each transformation

​

1. Parent graph g(x) = x³ Transformation g(x) + 4

​

​

• Parent graph p(x) = |x| Transformation p(x - 5)

​

​

• Parent graph m(x) = x² Transformation m(x + 1) - 2

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Heating the Kitchen

A bakery kitchen has a thermostat set to 65^oF. Starting at 5:00 a.m., the temperature in the kitchen rises to 85^oF (this takes an hour) when the ovens and other kitchen equipment are turned on to bake the daily breads and pastries. The ovens are turned off at 10:00 a.m. when the baking finishes. (It takes an hour to return to 65^oF)

1. Sketch a graph of the function H that gives the temperature in the kitchen H(x), in degrees Fahrenheit, x hours after midnight.

​

​

​

​

​

​

​

​

​

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Heating the Kitchen

Unit 5 ● Lesson 2 ● Activity 3

2. The bakery owner decides to change the shop hours to start and end 2 hours earlier. This means the daily baking schedule will also start and end two hours earlier. Sketch a graph of the new function G, which gives the temperature in the kitchen as a function of time.

​

​

​

​

​

​

​

​

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Heating the Kitchen

Unit 5 ● Lesson 2 ● Activity 3

3. Explain what H(10.25) = 80 means in this situation. Why is this reasonable?

4. If H(10.25) = 80, then what would the corresponding point on the graph of G be? Use function notation to describe the point on the graph of G.

5. Write an equation for G in terms of H. Explain why your equation makes sense.

​

​

​

​

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.