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 \( x = -6.5 \).