Question

For the following equation of a​ function, (a) find the zero of the​ function, (b) find the​ x-intercept of the graph of the​ function, and​ (c) solve the equation ​f(x)equals0.
​f(x)equals182plus28x

Answer 1

To analyze the function \( f(x) = 182 + 28x \), we can follow the steps outlined in your request:

### (a) Find the zero of the function:
To find the zero of the function, we set \( f(x) \) equal to zero and solve for \( x \):

\[
0 = 182 + 28x
\]

Subtract 182 from both sides:

\[
-182 = 28x
\]

Now, divide both sides by 28:

\[
x = \frac{-182}{28}
\]

Simplifying this fraction:

\[
x = -6.5
\]

So, the zero of the function is \( x = -6.5 \).

### (b) Find the x-intercept of the graph of the function:
The x-intercept of the graph of the function is the same as finding the zero of the function. Therefore, the x-intercept is:

\[
\text{x-intercept} = (-6.5, 0)
\]

### (c) Solve the equation \( f(x) = 0 \):
As we have already solved the equation in part (a), the solution is:

\[
x = -6.5
\]

### Summary:
- The zero of the function is \( x = -6.5 \).
- The x-intercept of the graph is \( (-6.5, 0) \).
- The solution to the equation \( f(x) = 0 \) is \( x = -6.5 \).