which input value produces the same output value for the two functions on the graph?\n$x = - 1$\n$x = 0$\n$x…

which input value produces the same output value for the two functions on the graph?\n$x = - 1$\n$x = 0$\n$x = 3$\n$x = 4$

which input value produces the same output value for the two functions on the graph?\n$x = - 1$\n$x = 0$\n$x = 3$\n$x = 4$

Answer

Answer:

C. (x = 3)

Explanation:

Step1: Understand the meaning of the same output value

The output value of a function for a given input (x) is the (y -)value. We need to find the (x) - value for which (f(x)=g(x)), that is, the (x) - coordinate of the point of intersection of the two graphs.

Step2: Analyze the point of intersection

Looking at the graph, the two functions (y = f(x)) (the horizontal line (y = 3)) and (y=g(x)) (the line with a slope) intersect at the point ((3,3)). At (x = 3), (f(3)=3) (since (f(x)=3) for all (x)) and (g(3)=3) (by substituting (x = 3) into the linear function (g(x))).

For (x=-1): (f(-1) = 3) and (g(-1)=-1) (using the equation of the line (y=\frac{1}{1}(x + 0)) (from the graph, slope (m = 1) and (y) - intercept (b = 0), (y=x))). For (x = 0): (f(0)=3) and (g(0)=0). For (x = 4): (f(4)=3) and (g(4)=4).