The function f(t)=-16t^2 +10 models the height (in feet) of an object t seconds after it is dropped from a height of 10 feet on Earth. The same object dropped from the same height on the moon is modeled by g(t)=-8/3t^2 +10. Describe the transformation of the graph f to obtain g.

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kathleen12 kathleen12 · Answer 1 · 2019-09-04T02:24:43+02:00

Vertically compressed by a factor of 1.22221667

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MrRoyal MrRoyal · Answer 2 · 2021-10-01T14:34:50+02:00

A transformed function would have some of its properties changed, after transformation.

The transformation from f(t) to g(t) is vertical compression by [tex]\frac{1}{ 6}[/tex]

Function f is given as:

[tex]f(t) = -16t^2 + 10[/tex]

Function g is given as:

[tex]g(t) = -\frac 83t^2 + 10[/tex]

The constant term (10) of both functions are the same.

This means that, the function is vertically compressed or stretched

Divide the coefficients of [tex]t^2[/tex] in both functions to calculate the factor of dilation

[tex]k = \frac{g(x)}{f(x)}[/tex]

So, we have:

[tex]k = \frac{-8/3}{-16}[/tex]

[tex]k = \frac{8/3}{16}[/tex]

Rewrite as:

[tex]k = \frac{8}{ 3 \times 16}[/tex]

[tex]k = \frac{1}{ 3 \times 2}[/tex]

[tex]k = \frac{1}{ 6}[/tex]

The scale factor is less than 1.

This represents vertical compression.

Hence, the transformation from f(t) to g(t) is vertical compression by [tex]\frac{1}{ 6}[/tex]