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 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 . 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 . The x- and y-intercepts are different for each function.
The function f(x) = x^3 + 1 has no y-intercept because when x = 0, f(x) = 1, so the point (0,1) is not on the graph.
The x-intercept can be found by setting f(x) = 0:
x^3 + 1 = 0
This equation does not have any real solutions, so there is no x-intercept for f(x).
The function g(x) = x + 1 has a y-intercept when x = 0:
g(0) = 0 + 1 = 1, so the point (0,1) is on the graph.
The x-intercept can be found by setting g(x) = 0:
x + 1 = 0
x = -1, so the x-intercept is (-1,0).
Therefore, the correct statement about the intercepts of the functions is:
Both functions have an x -intercept of (-1,0) and a y -intercept of (0,1).