Question

Given the function f(x)=log7x
, which of the following functions is the transformation of f(x)
9 units down, 5 units left, reflected across the x-axis, and stretched vertically by a factor of 8?(1 point)
Responses

g(x)=8log7(−x+5)−9
g left parenthesis x right parenthesis equals 8 logarithm subscript 7 baseline left parenthesis negative x plus 5 right parenthesis minus 9

g(x)=−8log7(x+5)−9
g left parenthesis x right parenthesis equals negative 8 logarithm subscript 7 baseline left parenthesis x plus 5 right parenthesis minus 9

g(x)=−8log7(x+9)−5
g left parenthesis x right parenthesis equals negative 8 logarithm subscript 7 baseline left parenthesis x plus 9 right parenthesis minus 5

g(x)=−8log7(x−5)−9

Answer 1

To determine the correct transformation of the function \( f(x) = \log_7 x \), we need to apply the following transformations step by step:

1. **Shift left by 5 units**: Replacing \( x \) with \( x + 5 \) results in \( \log_7(x + 5) \).
2. **Reflect across the x-axis**: Multiplying the function by -1 gives us \( -\log_7(x + 5) \).
3. **Stretch vertically by a factor of 8**: Multiplying by 8 results in \( -8\log_7(x + 5) \).
4. **Shift down by 9 units**: Subtracting 9 gives us \( -8\log_7(x + 5) - 9 \).

Now let's review the options:

1. \( g(x) = 8\log_7(-x + 5) - 9 \)
2. \( g(x) = -8\log_7(x + 5) - 9 \)
3. \( g(x) = -8\log_7(x + 9) - 5 \)
4. \( g(x) = -8\log_7(x - 5) - 9 \)

The correct transformation based on our steps is:

\[
g(x) = -8\log_7(x + 5) - 9
\]

Thus, the correct answer is:

**g(x) = -8log7(x + 5) - 9**