Question

What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(x + 5)? A) translate vertically 5 units up B) translate vertically 5 units down C) translate horizontally 5 units left D) translate horizontally 5 units right

Answer 1

Answer:

C) translate horizontally 5 units left

Step-by-step explanation:

f(x + 5)

Is a change in domain

The graph of f(x) is shifted 5 units towards the left to obtain the graph of f(x+5)

Answer 2

Answer:

C

Step-by-step explanation:

When we only change the x part of the function (that is, we add, subtract, multiply, or divide something in relation to the x part of f(x)), that is called a horizontal transformation. When we change the entire function, that's a vertical transformation.

In this case, because we are only changing the x (we turn f(x) into f(x + 5)), this is a horizontal transformation. One thing to note about horizontal transformations is that they are "backwards", which means that if we add to the x, we actually move the graph in the negative direction (which is to the left), whereas if we subtract from x, we move the graph in the positive direction (which is to the right).

Here, we're adding 5 to x, which we know means that we are translating the graph of f(x) horizontally to the left 5 units.

Thus, the answer is C.

Hope this helps!