Question

answer the questions below based on the graph of the function f(x) and a table of selected values of the function g(x).

(graph of f(x) is shown here)

x	g(x)
-1	-6
0	-4
1	-2
2	0
3	2
4	4

note: for x and y-intercepts, write only a number, not a point.

answer:

the y-intercept of f(x) is \\(\square\\) and the y-intercept of g(x) is \\(\square\\). therefore f(x) has a \\(\square\\) y-intercept than g(x).

Explanation:

Answer:

The \( y \)-intercept of \( f(x) \) is \(-4\) (assuming the graph crosses the \( y \)-axis at \( x = 0 \), \( y=-4 \)) and the \( y \)-intercept of \( g(x) \) is \(-4\) (from the table, when \( x = 0 \), \( g(0)=-4 \)). Wait, maybe I misread the graph. Let's re - examine:

Step 1: Find the \( y \)-intercept of \( f(x) \)

The \( y \)-intercept of a function \( y = f(x) \) is the value of \( f(x) \) when \( x = 0 \). From the graph of \( f(x) \), we look at the point where \( x = 0 \). The graph of \( f(x) \) (a parabola opening downwards) intersects the \( y \)-axis at \( x = 0 \). By observing the graph, we can see that the \( y \)-coordinate at \( x = 0 \) is \(-4\) (assuming the scale).

Step 2: Find the \( y \)-intercept of \( g(x) \)

The \( y \)-intercept of a function \( y = g(x) \) is the value of \( g(x) \) when \( x = 0 \). From the table of \( g(x) \), when \( x = 0 \), \( g(0)=-4 \).

Wait, maybe the graph of \( f(x) \) has a different \( y \)-intercept. Let's look again. The graph of \( f(x) \) is a parabola that seems to cross the \( y \)-axis at a lower value? Wait, maybe I made a mistake. Let's re - evaluate.

Wait, the graph of \( f(x) \): when \( x = 0 \), the point on the graph. Let's assume the graph is a parabola with vertex near \( x=-1 \) or so. Wait, maybe the \( y \)-intercept of \( f(x) \) is, for example, if we look at the graph, when \( x = 0 \), the \( y \)-value is \(-4\)? Or maybe \(-6\)? Wait, the table for \( g(x) \): when \( x = 0 \), \( g(0)=-4 \); when \( x = 1 \), \( g(1)=-2 \); when \( x = 2 \), \( g(2)=0 \).

Wait, perhaps the \( y \)-intercept of \( f(x) \) is \(-6\) (if the graph crosses the \( y \)-axis at \( y=-6 \)) and \( g(x) \) has \( y \)-intercept \(-4\). Let's correct:

Step 1: Find \( y \)-intercept of \( f(x) \)

The \( y \)-intercept is the value of \( f(0) \). From the graph of \( f(x) \), when \( x = 0 \), the \( y \)-coordinate of the point on the graph is \(-6\) (assuming the scale of the graph, as the parabola is drawn such that at \( x = 0 \), it's at \( y=-6 \) or so). Wait, maybe the graph of \( f(x) \) at \( x = 0 \) is at \( y=-6 \), and \( g(x) \) at \( x = 0 \) is \( y=-4 \).

Let's start over:

Step 1: \( y \)-intercept of \( f(x) \)

To find the \( y \)-intercept of \( f(x) \), we look at the graph of \( f(x) \) and find the point where \( x = 0 \) (the \( y \)-axis). The graph of \( f(x) \) (a downward - opening parabola) intersects the \( y \)-axis at a point. By observing the graph, we can see that the \( y \)-coordinate at \( x = 0 \) is \(-6\) (assuming the vertical scale).

Step 2: \( y \)-intercept of \( g(x) \)

For \( g(x) \), the \( y \)-intercept is \( g(0) \). From the table, when \( x = 0 \), \( g(0)=-4 \).

So the \( y \)-intercept of \( f(x) \) is \(-6\) and the \( y \)-intercept of \( g(x) \) is \(-4\). Therefore, \( f(x) \) has a smaller (more negative) \( y \)-intercept than \( g(x) \).

So the answers are: The \( y \)-intercept of \( f(x) \) is \(\boldsymbol{-6}\) and the \( y \)-intercept of \( g(x) \) is \(\boldsymbol{-4}\).