Question

You are given a table showing input and output values for a given function y 1equals​f(x). Using this​ table, find left parenthesis if possible right parenthesis ​(a) the​ x-intercept of the graph of yequals​f(x), ​(b) the​ y-intercept of the graph of yequals​f(x), ​and, (c) the solution to the equation ​f(x)equals0.
X
Upper Y 1
6
0
0
39
Question content area bottom
Part 1
​(a) What is the​ x-intercept? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
xequals
  
enter your response here
B.
There is no​ x-intercept.
Part 2
​(b) What is the​ y-intercept? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
yequals
  
enter your response here
B.
There is no​ y-intercept.
Part 3
​(c) What is the solution to ​f(x)equals​0? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
xequals
  
enter your response here
B.
There is no solution.

Answers

GPT-4o mini
Based on the table provided, it appears that \( f(x) \) is defined for at least two points. Here’s how to address each part of your question:

### Part 1: X-Intercept
The x-intercept occurs where \( f(x) = 0 \). From the provided values, if \( f(x) = 0 \) corresponds to \( x = 6 \) (since the output \( y \) is zero at this point), we can conclude:

- **(a)** The x-intercept is:
- A. \( x = 6 \)

### Part 2: Y-Intercept
The y-intercept occurs where \( x = 0 \). From the provided values, \( f(0) = 39 \). Therefore:

- **(b)** The y-intercept is:
- A. \( y = 39 \)

### Part 3: Solution to \( f(x) = 0 \)
The solution to the equation \( f(x) = 0 \) is the same as the x-intercept, which we found to occur at \( x = 6 \). Thus:

- **(c)** The solution to \( f(x) = 0 \) is:
- A. \( x = 6 \)

### Summary
So final answers are:
- **(a)** \( x = 6 \)
- **(b)** \( y = 39 \)
- **(c)** \( x = 6 \)