Question

Use the properties of exponents to rewrite the function f(x)=351−x+7
in the form f(x)=a(b)x−h+k
.(1 point)
$$

Answer 1

To rewrite the function \( f(x) = 351^{-x} + 7 \) in the form \( f(x) = a(b)^{x-h} + k \), we will first manipulate the expression.

### Step 1: Rewrite the function
The expression \( 351^{-x} \) can be rewritten using the property of exponents that states \( a^{-b} = \frac{1}{a^b} \):
\[
f(x) = \frac{1}{351^x} + 7
\]

### Step 2: Rewrite in exponential form
We can express \( \frac{1}{351^x} \) as \( 351^x \) raised to a negative exponent:
\[
f(x) = 351^{-x} + 7
\]

### Step 3: Identify parameters for the desired form
Now, let's identify \( a \), \( b \), \( h \), and \( k \) for \( f(x) = a(b)^{x-h} + k \):
1. Recognize that \( a = 1 \) (as the leading coefficient of the exponential term).
2. The base \( b = 351 \).
3. The exponent is affected by \( -x \), which implies \( h = 0 \) (as there is no horizontal shift).
4. The vertical shift \( k = 7 \).

### Final expression
Thus, we can rewrite:
\[
f(x) = 1(351)^{-x-0} + 7
\]
or simply:
\[
f(x) = 1 \cdot 351^{-x} + 7
\]

### Conclusion
In conclusion, the function can be written in the desired form as:
\[
f(x) = 1 \cdot 351^{-x} + 7
\]
where \( a = 1 \), \( b = 351 \), \( h = 0 \), and \( k = 7 \).