Question

HELP ASAP 100 POINTS!!!

The table of values represents the function g(x) and the graph shows the function f(x).
Which statement about the functions is true?

1. f(x) is greater than g(x) for all values of x.

2. f(x) and g(x) have the same y-intercept.

3. f(x) and g(x) intersect at two points.

4.f(x) and g(x) have a common x-intercept.

Answer 1

The answer is choice 4

Answer 2

Answer: choice 4. f(x) and g(x) have a common x-intercept

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Step-by-step explanation:

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

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Side notes:

• Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
• Choice 2 is not true. Point B is not on the parabola.
• Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.