Question
You are given a table showing input and output values for a given function y 1equalsf(x). Using this table, find left parenthesis if possible right parenthesis (a) the x-intercept of the graph of yequalsf(x), (b) the y-intercept of the graph of yequalsf(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)equals0? 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.
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)equals0? 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)** \( x = 6 \)
### 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)** \( x = 6 \)