Question
Use the table to answer the question.
x f(x)=x3+1
g(x)=x+1
−2
−7
−1
−1
0 0
0 1 1
1 2 2
2 9 3
Compare the functions f(x)=x3+1
and g(x)=x+1
. Which of the following statements is true about the intercepts of the functions?
(1 point)
Responses
Both functions have a y-intercept of (−1,0)
and an x-intercept of (0,1)
.
Both functions have a y -intercept of left parenthesis negative 1 comma 0 right parenthesis and an x -intercept of left parenthesis 0 comma 1 right parenthesis .
The x- and y-intercepts are different for each function.
The x - and y -intercepts are different for each function.
The graphs intersect at (1,2)
.
The graphs intersect at left parenthesis 1 comma 2 right parenthesis .
Both functions have an x-intercept of (−1,0)
and a y-intercept of (0,1)
.
x f(x)=x3+1
g(x)=x+1
−2
−7
−1
−1
0 0
0 1 1
1 2 2
2 9 3
Compare the functions f(x)=x3+1
and g(x)=x+1
. Which of the following statements is true about the intercepts of the functions?
(1 point)
Responses
Both functions have a y-intercept of (−1,0)
and an x-intercept of (0,1)
.
Both functions have a y -intercept of left parenthesis negative 1 comma 0 right parenthesis and an x -intercept of left parenthesis 0 comma 1 right parenthesis .
The x- and y-intercepts are different for each function.
The x - and y -intercepts are different for each function.
The graphs intersect at (1,2)
.
The graphs intersect at left parenthesis 1 comma 2 right parenthesis .
Both functions have an x-intercept of (−1,0)
and a y-intercept of (0,1)
.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the intercepts of the functions \( f(x) = x^3 + 1 \) and \( g(x) = x + 1 \), we can find both the x-intercepts and y-intercepts for each function.
### For \( f(x) = x^3 + 1 \):
- **Y-Intercept**: Set \( x = 0 \):
\[
f(0) = 0^3 + 1 = 1
\]
So, the y-intercept is \( (0, 1) \).
- **X-Intercept**: Set \( f(x) = 0 \):
\[
x^3 + 1 = 0 \implies x^3 = -1 \implies x = -1
\]
So, the x-intercept is \( (-1, 0) \).
### For \( g(x) = x + 1 \):
- **Y-Intercept**: Set \( x = 0 \):
\[
g(0) = 0 + 1 = 1
\]
So, the y-intercept is \( (0, 1) \).
- **X-Intercept**: Set \( g(x) = 0 \):
\[
x + 1 = 0 \implies x = -1
\]
So, the x-intercept is \( (-1, 0) \).
### Summary of Intercepts:
- For \( f(x) = x^3 + 1 \):
- X-Intercept: \( (-1, 0) \)
- Y-Intercept: \( (0, 1) \)
- For \( g(x) = x + 1 \):
- X-Intercept: \( (-1, 0) \)
- Y-Intercept: \( (0, 1) \)
### Conclusion:
Both functions have the same x-intercept at \( (-1, 0) \) and the same y-intercept at \( (0, 1) \).
Therefore, the true statement is:
**Both functions have an x-intercept of \( (-1, 0) \) and a y-intercept of \( (0, 1) \).**
### For \( f(x) = x^3 + 1 \):
- **Y-Intercept**: Set \( x = 0 \):
\[
f(0) = 0^3 + 1 = 1
\]
So, the y-intercept is \( (0, 1) \).
- **X-Intercept**: Set \( f(x) = 0 \):
\[
x^3 + 1 = 0 \implies x^3 = -1 \implies x = -1
\]
So, the x-intercept is \( (-1, 0) \).
### For \( g(x) = x + 1 \):
- **Y-Intercept**: Set \( x = 0 \):
\[
g(0) = 0 + 1 = 1
\]
So, the y-intercept is \( (0, 1) \).
- **X-Intercept**: Set \( g(x) = 0 \):
\[
x + 1 = 0 \implies x = -1
\]
So, the x-intercept is \( (-1, 0) \).
### Summary of Intercepts:
- For \( f(x) = x^3 + 1 \):
- X-Intercept: \( (-1, 0) \)
- Y-Intercept: \( (0, 1) \)
- For \( g(x) = x + 1 \):
- X-Intercept: \( (-1, 0) \)
- Y-Intercept: \( (0, 1) \)
### Conclusion:
Both functions have the same x-intercept at \( (-1, 0) \) and the same y-intercept at \( (0, 1) \).
Therefore, the true statement is:
**Both functions have an x-intercept of \( (-1, 0) \) and a y-intercept of \( (0, 1) \).**
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