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

1 answer

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 \( x = -6.5 \).