standard_description: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Problem 1
You and a friend are going for a run along a path. You both run at the same exact speed, but your friend starts 100 yards ahead of the starting point which is where you start.
The graph below is a sketch of your and your friend’s distance traveled from the starting point over time. When will you and your friend be the same distance from the starting point? Explain your answer using the graph.
[IMG]
Problem 2
Graph the system of equations below.
| $${y={1\over3}(x-6)}$$                        $${6y=2x-12}$$ | .. image:: https://d21royfkw9g4l6.cloudfront.net/uploads/2022/09/23/slice-1-2022-09-23t114209772.png |
|--------------------------------------------------------------|------------------------------------------------------------------------------------------------------|
Anika was not sure how to interpret the graph of the system. She thought that since there was only one line visible in the graph then there were no solutions to the system of equations. Do you agree with Anika's reasoning? Explain why or why not.
Problem 3
Consider the equation
$$y = \frac{2}{5} x + 1$$
. Write a second linear equation to create a system of equations that has:
a.   Exactly one solution
b.   No solutions
c.   Infinite solutions


aligns: no