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I’m so confused..? how do u write a function for this..?

I’m so confused..? how do u write a function for this..?-example-1

1 Answer

3 votes

Answer:


\boxed{y=h(x)=4x^2-5}

Explanation:

Nonrigid transformations are those causing a distortion or a change in the shape of the original graph. Stretching a graph are part of nonrigid transformations. On the other hand, rigid transformations are those where the basic shape of the graph is unchanged. Translations are part of rigid transformations.

If
y=f(x) then
g(x)=cf(x) represents a vertical stretch if
c>1. In this case
c=4.

Since
y=g(x)=x^2, the:


  • g(x)=4x^2 represents that the function is vertically stretched by a factor of 4

For translating a graph k units downward we have:


\bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \ h(x)=f(x)-k

Therefore,
k=5 and translating the previous graph 5 units downward is:


\boxed{y=h(x)=4x^2-5}

Finally, this
h(x) is the function we are looking for.

User Prudhvi
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