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
10
0
0
27
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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
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.
X
Upper Y 1
10
0
0
27
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
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
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.
Answers
GPT-4o mini
Based on the table you provided, it appears there are input-output pairs for the function \( y = f(x) \). However, the formatting is a bit unclear. Let’s clarify the given input and output values:
- \( x = 10 \) and \( y = 0 \)
- \( x = 0 \) and \( y = 27 \)
Now, let's address your questions:
(a) **The x-intercept of the graph of \( y = f(x) \)**:
- The x-intercept occurs when \( y = 0 \). From the table, when \( x = 10 \), \( y = 0 \). Therefore, the x-intercept is:
\[
\text{The x-intercept is } (10, 0).
\]
(b) **The y-intercept of the graph of \( y = f(x) \)**:
- The y-intercept occurs when \( x = 0 \). From the table, when \( x = 0 \), \( y = 27 \). Therefore, the y-intercept is:
\[
\text{The y-intercept is } (0, 27).
\]
c) **The solution to the equation \( f(x) = 0 \)**:
- The solution to the equation \( f(x) = 0 \) is the same as finding the x-intercept. As we established, \( f(x) = 0 \) occurs when \( x = 10 \).
Therefore, the solution is:
\[
\text{The solution to } f(x) = 0 \text{ is } x = 10.
\]
In summary:
- **x-intercept**: \( (10, 0) \)
- **y-intercept**: \( (0, 27) \)
- **Solution to** \( f(x) = 0 \): \( x = 10 \)
- \( x = 10 \) and \( y = 0 \)
- \( x = 0 \) and \( y = 27 \)
Now, let's address your questions:
(a) **The x-intercept of the graph of \( y = f(x) \)**:
- The x-intercept occurs when \( y = 0 \). From the table, when \( x = 10 \), \( y = 0 \). Therefore, the x-intercept is:
\[
\text{The x-intercept is } (10, 0).
\]
(b) **The y-intercept of the graph of \( y = f(x) \)**:
- The y-intercept occurs when \( x = 0 \). From the table, when \( x = 0 \), \( y = 27 \). Therefore, the y-intercept is:
\[
\text{The y-intercept is } (0, 27).
\]
c) **The solution to the equation \( f(x) = 0 \)**:
- The solution to the equation \( f(x) = 0 \) is the same as finding the x-intercept. As we established, \( f(x) = 0 \) occurs when \( x = 10 \).
Therefore, the solution is:
\[
\text{The solution to } f(x) = 0 \text{ is } x = 10.
\]
In summary:
- **x-intercept**: \( (10, 0) \)
- **y-intercept**: \( (0, 27) \)
- **Solution to** \( f(x) = 0 \): \( x = 10 \)