Question

If k(x)=3x
is vertically stretched with a factor of 5, shifted down 7 units, and reflected across the y-axis, which of the following functions denotes the given transformations?(1 point)
Responses

k(x)=15⋅3−x−7
k left parenthesis x right parenthesis equals Start Fraction 1 over 5 End Fraction times 3 superscript negative x baseline minus 7

k(x)=5⋅3−x−7
k left parenthesis x right parenthesis equals 5 times 3 superscript negative x baseline minus 7

k(x)=−5⋅3x−7
k left parenthesis x right parenthesis equals negative 5 times 3 superscript x baseline minus 7

k(x)=5⋅3−x+7

Answer 1

Let's apply the transformations step-by-step to the original function \( k(x) = 3x \).

1. **Vertically stretched with a factor of 5**:
This means we multiply the function by 5:
\[
k(x) = 5 \cdot 3^x
\]

2. **Shifted down 7 units**:
We subtract 7 from the function:
\[
k(x) = 5 \cdot 3^x - 7
\]

3. **Reflected across the y-axis**:
To reflect across the y-axis, we replace \( x \) with \( -x \):
\[
k(x) = 5 \cdot 3^{-x} - 7
\]

Combining all transformations, the resulting function is:
\[
k(x) = 5 \cdot 3^{-x} - 7
\]

So the correct answer from the given options is:
\[
k(x) = 5 \cdot 3^{-x} - 7
\]
which matches the option:
\[
\text{k left parenthesis x right parenthesis equals 5 times 3 superscript negative x baseline minus 7}
\]