What transformations change the graph of f(x) to the graph of g(x)? f(x) = -7x², g(x) = -35x² + 5

Solution:

Given, functions are f(x) = -7x²

g(x) = -35x² + 5

We have to find the transformation that changes the graph of f(x) to g(x).

The transformation to the graph is given by y = a[f(x)]

If a > 1, the graph of y = f(x) os expanded vertically by a factor a.

When a = 5

y = 5(f(x))

y = 5(-7x²)

y = -35x²

The translation to the graph is given by y = f(x) + k

If k > 0 the graph moves k units up.

When k = 5

y = -35x² + 5

y = g(x)

Therefore, the graph f(x) is moved vertically by a factor of 5 and translated up to 5 units.

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What transformations change the graph of f(x) to the graph of g(x)? f(x) = -7x², g(x) = -35x² + 5

Summary:

The transformation that changes the graph of f(x) = -7x² to the graph of g(x) = -35x² + 5 is f(x) is moved vertically by a factor of 5 and translated upto 5 units.