Answer: D. f(x) has a higher intercept
Step-by-step explanation:
From the graph, we can see that the line crosses the y-axis at 2 so the y-intercept of f(x) is 2.
From the table, we can find the slope using the slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] Then input the slope (m) and one of the points (x₁, y₁) into the Point-Slope formula and solve for "y" so the equation is in y = mx + b format.
(x₁, y₁) = (1, 0) and (x₂, y₂) = (3, 4)
[tex]m=\dfrac{4-0}{3-1}\\\\.\quad =\dfrac{4}{2}\\\\.\quad =2\\\\\text{Point-Slope format is:}\ y - y_1 = m(x - x_1)\\\\y = 0 = 2(x - 1)\\\\y = 2x - 2\\\\\text{So, the y-intercept (b) for g(x) is -2}[/tex]
f(x) = 2 < g(x) = -2
