Question

The graph of g(x) is the result of translating the graph of f(x) (1\2)x = three units to the left. What is the equation of g(x)?

Answer 1

The equation $f(x)= \frac{1}{2}x$ is plotted on graph below (red line)

Translating $f(x)$ three units to the left can be done by choosing  any coordinates on $f(x)$.

Let choose (0,0) and (2,1)
Translating 3 units on to the left gives the new coordinates (0-3, 0)=(-3,0) and (2-3, 1)=(-1, 1)

The gradient of the two functions will stay the same since the lines are parallel to each other, so m = 0.5

By joining the two coordinates (-3,0) and (-1,1), we see that the translated line crosses y-axis at 1.5

The equation of translated line is given
$g(x)=0.5(x-(-3))$
$g(x)=0.5(x+3)$
$g(x)=0.5x+1.5$