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
negative 10
0
0
38
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
negative 10
0
0
38
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
To solve the questions you provided, we need to analyze the provided table data. However, it seems like there may be some missing details regarding the values in the table. Let's assume the data represents the function values in the following way based on your indications:
- For \( x = -10 \), \( f(x) = 0 \) (which means \( y \) is 0 at \( x = -10 \)).
- For \( x = 0 \), \( f(x) = 38 \) (which means \( y \) is 38 at \( x = 0 \)).
Now we can address each part of the question:
### Part 1: Finding the x-intercept.
The x-intercept occurs where \( y = f(x) = 0 \).
From the table, we see:
- When \( x = -10 \), \( f(x) = 0 \).
Thus, the x-intercept is:
**A. \( x = -10 \)**
### Part 2: Finding the y-intercept.
The y-intercept occurs where \( x = 0 \).
From the table, we see:
- When \( x = 0 \), \( f(x) = 38 \).
Thus, the y-intercept is:
**A. \( y = 38 \)**
### Part 3: Finding the solution to \( f(x) = 0 \).
The solution to the equation \( f(x) = 0 \) is the same as the x-intercept because it indicates the values of \( x \) for which \( y \) is 0.
From our earlier analysis, we found that:
**A. \( x = -10 \)**
Summary:
- **(a)** \( x = -10 \)
- **(b)** \( y = 38 \)
- **(c)** \( x = -10 \)
- For \( x = -10 \), \( f(x) = 0 \) (which means \( y \) is 0 at \( x = -10 \)).
- For \( x = 0 \), \( f(x) = 38 \) (which means \( y \) is 38 at \( x = 0 \)).
Now we can address each part of the question:
### Part 1: Finding the x-intercept.
The x-intercept occurs where \( y = f(x) = 0 \).
From the table, we see:
- When \( x = -10 \), \( f(x) = 0 \).
Thus, the x-intercept is:
**A. \( x = -10 \)**
### Part 2: Finding the y-intercept.
The y-intercept occurs where \( x = 0 \).
From the table, we see:
- When \( x = 0 \), \( f(x) = 38 \).
Thus, the y-intercept is:
**A. \( y = 38 \)**
### Part 3: Finding the solution to \( f(x) = 0 \).
The solution to the equation \( f(x) = 0 \) is the same as the x-intercept because it indicates the values of \( x \) for which \( y \) is 0.
From our earlier analysis, we found that:
**A. \( x = -10 \)**
Summary:
- **(a)** \( x = -10 \)
- **(b)** \( y = 38 \)
- **(c)** \( x = -10 \)