Question

Based on the graph of the function,f(x)

Answer 1

(A ) This is a straight line graph.

The equation of a straight line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m  = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 1 ) and (x₂, y₂ ) = (-2, - 3 ) ← 2 points on the line

m = $\frac{-3-1}{-2-0}$ = $\frac{-4}{-2}$ = 2

The y-intercept = (0, 1 ) ⇒ c = 1

f(x) = 2x + 1 ← function rule

(B)

To evaluate f(2), substitute x = 2 into the rule

f(2) = (2 × 2 ) + 1 = 4 + 1 = 5

As a check (2, 5 ) is a point on the graph