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

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⋅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

To find the function that represents the transformations applied to \( k(x) = 3x \), we need to apply the given transformations step by step:

1. **Vertical Stretch by a Factor of 5**:
- This multiplies the function by 5.
\[
k(x) = 5 \cdot 3^x
\]

2. **Reflection Across the Y-Axis**:
- This changes \( x \) to \( -x \).
\[
k(x) = 5 \cdot 3^{-x}
\]

3. **Shift Down 7 Units**:
- This subtracts 7 from the entire function.
\[
k(x) = 5 \cdot 3^{-x} - 7
\]

Putting it all together, the final transformed function is:

\[
k(x) = 5 \cdot 3^{-x} - 7
\]

Thus, the correct answer from your options is:

**k(x) = 5 ⋅ 3^(-x) - 7**.