Question

The function f(x)=x3
is stretched vertically, and the resulting function is g(x)=af(x)
. Identify which of the following values of a could be responsible for this transformation.(1 point)
Responses

0.10
0.10

1.03
1.03

1
1

0.03
0.03

Answer 1

When a function \( f(x) \) is stretched vertically by a factor of \( a \) to obtain the new function \( g(x) = af(x) \), the value of \( a \) determines whether the transformation stretches or compresses the graph of the function.

1. If \( a > 1 \), the function is stretched vertically.
2. If \( 0 < a < 1 \), the function is compressed vertically.
3. If \( a = 1 \), there is no transformation.
4. If \( a < 0 \), the function is reflected and can also be stretched or compressed.

In the options provided:

- \( 0.10 \): This value is between 0 and 1, so it would compress the function.
- \( 1.03 \): This value is greater than 1, so it would stretch the function.
- \( 1 \): This indicates no transformation.
- \( 0.03 \): This value is also between 0 and 1, so it would compress the function.

The value of \( a \) that could be responsible for a vertical stretch of the function \( f(x) = x^3 \) to obtain \( g(x) = af(x) \) is **1.03**.