Cumulative Assessment
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Rewrite each transformation using the parent function, f(x), and then compare them to the graph.
g(x), h(x), k(x), and q(x)
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 |
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) |