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

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).
Both functions have an x -intercept of left parenthesis negative 1 comma 0 right parenthesis and a y -intercept of left parenthesis 0 comma 1 right parenthesis .

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.

Answer 1

To compare the functions \( f(x) = x^3 + 1 \) and \( g(x) = x + 1 \) using their intercepts:

1. **Finding x-intercepts** (where \( y = 0 \)):
- For \( f(x) = 0 \):
\[
x^3 + 1 = 0 \implies x^3 = -1 \implies x = -1
\]
So, \( f(x) \) has an x-intercept at \( (-1, 0) \).

- For \( g(x) = 0 \):
\[
x + 1 = 0 \implies x = -1
\]
So, \( g(x) \) also has an x-intercept at \( (-1, 0) \).

2. **Finding y-intercepts** (where \( x = 0 \)):
- For \( f(0) \):
\[
f(0) = 0^3 + 1 = 1
\]
So, \( f(x) \) has a y-intercept at \( (0, 1) \).

- For \( g(0) \):
\[
g(0) = 0 + 1 = 1
\]
So, \( g(x) \) also has a y-intercept at \( (0, 1) \).

### Summary of Intercepts:
- Both functions have an x-intercept at \( (-1, 0) \).
- Both functions have a y-intercept at \( (0, 1) \).

### Conclusion:
The correct statement is:
**Both functions have an x-intercept of (−1,0) and a y-intercept of (0,1).**