Transformations: The graph of h(x) is a reflection in the x-axis, followed by a vertical stretch by a factor of 3, and a vertical translation 4 units down of the graph of f(x). Graph:
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How does the equation of h(x) differ from f(x)? Let's see!
f(x)&=x
h(x)&= - 3x - 4
We can see that x was multiplied by -3. Therefore, we can say it was first multiplied by -1 and transformed to h_1(x)=- x. This is a reflection in the x-axis.
Then, h_1(x) was multiplied by 3 and transformed to h_2(x)=-3 x. Let's see it on a graph!
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 farther 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 4 units down. Any shift in the vertical or horizontal direction is a translation. In this case, we have a vertical translation down by 4.
