Cumulative Assessment
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Rewrite each transformation using the parent function, f(x), and then compare them to the graph.
Functions: g(x), h(x), k(x), and q(x)
Explanation: See solution.
Let's begin by figuring out how each transformation affects the parent function, f(x)=x-1.
| Transformed Function | f(x)→? | Simplified |
|---|---|---|
| g(x)=f( x+2) | ( x+2)-1 | g(x)=x+1 |
| k(x)=f(x) + 4 | (x-1) + 4 | k(x)=x+3 |
| r(x)= 3f(x) | 3(x-1) | r(x)=3x-3 |
| h(x)=f( 3x) | 3x-1 | h(x)=3x-1 |
| p(x)=f( - x) | - x-1 | p(x)=- x-1 |
| q(x)= - f(x) | -(x-1) | q(x)=- x+1 |
Now, we can look at the given graph and find the slope and y-intercept for each function.
We can then compare these requirements to the equations that we just found.
| Function Color | Slope | y-intercept | Equation | Corresponding Function |
|---|---|---|---|---|
| Blue | -1 | 1 | y=- x+1 | q(x) |
| Red | 3 | -1 | y=3x-1 | h(x) |
| Green | 1 | 1 | y=x+1 | g(x) |
| Purple | 1 | 3 | y=x+3 | k(x) |