Question

If f(x)=7x is horizontally stretched by a factor of 5, moved up 3 units, and reflected across the x-axis, which of the following is the new expression of f(x)? (1 point) Responses f(x)=−75x+3 f of x is equal to negative 7 raised to the 5 x power plus 3 f(x)=−715x+3 f of x is equal to negative 7 raised to the 1 fifth x power plus 3 f(x)=15⋅7−x+3 f of x is equal to 1 fifth times 7 raised to the negative x power plus 3 f(x)=−5⋅7x+3

Answer 1

To find the new expression for \( f(x) = 7x \) after applying the transformations, let's go through each transformation step-by-step:

1. **Horizontally stretched by a factor of 5**:
To stretch horizontally by a factor of 5, we replace \( x \) with \( \frac{x}{5} \):
\[
f(x) = 7\left(\frac{x}{5}\right) = \frac{7}{5}x
\]

2. **Reflected across the x-axis**:
To reflect the function across the x-axis, we multiply the entire function by -1:
\[
f(x) = -\frac{7}{5}x
\]

3. **Moved up 3 units**:
To move the function up by 3 units, we add 3 to the entire function:
\[
f(x) = -\frac{7}{5}x + 3
\]

Now, let's match this with the given options. We have:
\[
f(x) = -\frac{7}{5}x + 3
\]

The correct expression corresponding to this transformation is:
\[
f(x) = -\frac{7}{5}x + 3
\]

Thus, the correct answer from the choices is:
**f(x)=−715x+3**.