When you look at the graph of h(x), how does the y-intercept differ from f(x)? What transformation could cause this shift?
Transformations: The graph of h(x) is a vertical stretch by a factor of 3 and a vertical translation 5 units down of the graph of f(x). Graph:
Practice makes perfect
Let's begin by graphing both functions. Then we can compare the differences between them to determine what transformations may have taken place.
First, look at how the slope changes between f(x) and h(x).
Looking at the slope triangles, we can see that the rise in f(x) is 3 times smaller than the rise in h(x). This means that h(x) is moving away from the x-axis 3 times faster than f(x).
Slope off(x):&2 ⇔ rise/run=6/3 [0.8em]
Slope ofh(x):&6 ⇔ rise/run=18/3
When a function is pulled away from or pushed towards the x-axis, this is either a vertical stretch or shrink. Because the transformed function is further away from the x-axis, it is a vertical stretch by a factor of 3. The next thing to notice is how the y-intercept changes.
The y-intercept moved 5 units down. Any shift in the vertical or horizontal direction is a translation. In this case, we have a vertical translation down by 5.
