Question

Question The graph of g(x) is a transformation of the graph of f(x)=3x. Enter the equation for g(x) in the box. g(x) =

Answer 1

After the specified transformations, the equation for
`\( g(x) \) is \( g(x) = 3x \).`

Given that the graph of
`\( g(x) \)` is a transformation of the graph of
`\( f(x) = 3x \)` involving a horizontal compression by a factor of
`\( (1)/(2) \)` followed by a vertical stretch by a factor of 2, the equation for
`\( g(x) \)`can be obtained as follows:

1. Horizontal Compression by
`\( (1)/(2) \)` : Multiply the variable
`\( x \) in \( f(x) \)`by
`\( (1)/(2) \).`

`\[ f_1(x) = 3 \left((1)/(2)x\right) \]`

2. Vertical Stretch by 2: Multiply the entire function by 2.

`\[ g(x) = 2 \cdot f_1(x) \]`

Combine these steps:

`\[ g(x) = 2 \cdot 3 \left((1)/(2)x\right) \]`

Simplify further:

`\[ g(x) = 3x \]`

Therefore, after the specified transformations, the equation for
`\( g(x) \)`is
`\( g(x) = 3x \).`