Algebra 1 4.07 Honors Activity Part C

4.07 Project: Demonstration

407 Project Procedure Instructions 0:43 min

On the LEFT SIDE, I will demonstrate and model regarding the example scenario.

4.07 Project: Your Work

On the RIGHT SIDE, you will write the answers and show the work to your scenario. PAUSE THE VIDEOS AS NEEDED TO COMPLETTHIS SIDE ON YOUR OWN, USING THE MODELED SCENARIO ON THE RIGHT!!

Writing and Verifying Inverse Functions

Writing and Verifying Inverse Functions

7:08

a) Use the given function to create its inverse.

Make Sure You Notice This! 0:53 min

f(x)=x + 43

b) Show your work to prove that the inverse of f(x) is g(x).

c) Show your work to evaluate g(f(x)).

d) Graph your two functions on a coordinate plane. Include a table of values for each function.

x

f(x)=

g(x)=

Task #1

Part 1:

Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.

f(x)=x + ab

g(x) = cx - d

Part 2:

Show your work to prove that the inverse of f(x) is g(x).

Part 3:

Show your work to evaluate f(g(x)).

Part 4:

Graph your two functions on a coordinate plane. Include a table of values for each function. Graph the line y = x on the same graph.

x

f(x)=

g(x)=

2

3

4

5

https://www.desmos.com/calculator

Radical Equations With and Without Extraneous Solutions

Radical Equations With and Without Extraneous Solutions

6:32

a) Make two radical equations. One must have an extraneous solution and the other does not.

b) Solve the equation. Check your solution.

c) Explain why one equation has an extraneous solution and the other does not.

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Task #2

Part 1:

Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:

ax+b+c=d

Use a constant in place of each variable a, b, c, and d. You can use positive and negative constraints in your equation.

Part 2:

Show your work in solving the equation. Include your work to check your solution and show that your solution is extraneous.

Part 3:

Explain why the first equation has an extraneous solution and the second does not.