Question

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answer 1

Using the points stated in the original problem, I have determined the lines for the graph.

f(x)=3x-1

g(x)= 3x+17

Using the basic descriptions of transformations, we can determine the movement of the lines as being either horizontal or vertical shifts.

(to put a visual to this problem, I the diagram in Desmos and then marked the stated points on the graph.)

Horizontal shifts move the line either to the left or to the right.

Vertical shifts move the line either up or down.

If you look at the graphs as being the same x-value for the functions, the change in the y- value is +18, which is a vertical shift.

If you look at the graphs as being the same y-values, the change in x is -6 which is a horizontal shift.

So, the value of k is the amount of change each equation has to have to match the points given. (from f(x) to g(x))

The vertical shift is g(x)=f(x) +18

The horizontal shift is g(x)=f(x-6)