Question

in the attached diagram a sketch of the function () = −4 = 2i) Sketch all the following on the attached diagram, ensuring that you distinguish between your answers.a) () + 2b) (− )c) 2()ii) What type of function is this, explain your answer clearly.

Answer 1

i) Graph

ii) Exponential function

Step-by-step explanation:

First, we can see that there is only one function that is in the opposite direction. It is decreasing when the others are increasing. It means that this function is f(-x). This is because f(-x) is a reflection over the y-axis of f(x). So, we can identify f(-x) and f(x) because they are the functions that cross in the y-axis.

Then, knowing which one is f(x), f(x) + 2 will be the same function but 2 units up. So, if f(x) pass through (0, 1), f(x) + 2 will pass throug (0, 3) because it is located 2 units up because

1 + 2 = 3

In the same way, 2f(x), makes double the y-coordinate, so if f(x) pass through (0, 1), 2f(x) will pass through (0, 2) because

2(1) = 2

As a review, we know that

If we have f(x) + c, we move c units up.

If we have f(x) - c, we move c units down

If we have f(x - c), we move c units to the right

If we have f(x + c), we move c units to the left

Finally, we can identify each diagram as follows

Finally, this function is an exponential function because it is increasing and have this curve path.