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 4
0
0
32
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 4
0
0
32
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 answer your questions, we need to analyze the given data from the table. From your data, we can summarize the input and output values as follows:
- At \( x = -4 \), \( y = f(-4) = 0 \)
- At \( x = 0 \), \( y = f(0) = 32 \)
Now, let's address each part:
### Part 1: x-intercept
**Definition**: The x-intercept of a function is the value of \( x \) at which \( f(x) = 0 \).
From the data:
- At \( x = -4 \), \( f(-4) = 0 \).
Thus, the x-intercept is:
- **Answer**: \( x = -4 \)
### Part 2: y-intercept
**Definition**: The y-intercept of a function is the value of \( y \) when \( x = 0 \).
From the data:
- At \( x = 0 \), \( f(0) = 32 \).
Thus, the y-intercept is:
- **Answer**: \( y = 32 \)
### Part 3: Solution to the equation \( f(x) = 0 \)
This is the same question as asking for the x-intercept because we are looking for the values of \( x \) that make \( f(x) = 0 \).
From the data:
- As determined, \( f(-4) = 0 \).
Thus, the solution to \( f(x) = 0 \) is:
- **Answer**: \( x = -4 \)
### Summary of Answers
- **(a)** \( x = -4 \) (X-intercept)
- **(b)** \( y = 32 \) (Y-intercept)
- **(c)** \( x = -4 \) (Solution to \( f(x) = 0 \))
- At \( x = -4 \), \( y = f(-4) = 0 \)
- At \( x = 0 \), \( y = f(0) = 32 \)
Now, let's address each part:
### Part 1: x-intercept
**Definition**: The x-intercept of a function is the value of \( x \) at which \( f(x) = 0 \).
From the data:
- At \( x = -4 \), \( f(-4) = 0 \).
Thus, the x-intercept is:
- **Answer**: \( x = -4 \)
### Part 2: y-intercept
**Definition**: The y-intercept of a function is the value of \( y \) when \( x = 0 \).
From the data:
- At \( x = 0 \), \( f(0) = 32 \).
Thus, the y-intercept is:
- **Answer**: \( y = 32 \)
### Part 3: Solution to the equation \( f(x) = 0 \)
This is the same question as asking for the x-intercept because we are looking for the values of \( x \) that make \( f(x) = 0 \).
From the data:
- As determined, \( f(-4) = 0 \).
Thus, the solution to \( f(x) = 0 \) is:
- **Answer**: \( x = -4 \)
### Summary of Answers
- **(a)** \( x = -4 \) (X-intercept)
- **(b)** \( y = 32 \) (Y-intercept)
- **(c)** \( x = -4 \) (Solution to \( f(x) = 0 \))