Question

Im having so much trouble with this question, someone help pls :(

For each function shown:

Name the starting point.
Explain how y changes as x increases.
Function #1: y = 0.5 + 3x
Function #2: y = 3(0.5)^x

Answer 1

Any ideas?

Answer 2

Let's begin with function #1

y = 0.5 + 3x

The question asks "what is the 'starting' point"?

Think about that. What does it mean to start at a point?

You need to "assume" that x starts at some number, say the numerical 0 is a good choice.

So, now replace x with 0 in the defining equation of the function to give you the "starting value" of y.

y = 0.5 + 3x
y = 0.5 + 3•(0)
y = 0.5 + 0
y = 0.5

So, this gives you the "starting point"
(x, y) = (0, 0.5).

Answer 3

Any questions?

:-)

Answer 4

Use the exact same procedure to find the starting point for function #2

Answer 5

The second part of the question asks for an explanation of how y changes as x increases.

To explain this it's best to draw a graph. But where do we start? Let's use the starting point calculated from the first part of the question for y = 0.5 + 3x we calculated that (0, 0.5) was the starting point, let's replace x with the number 1 and see what happens to y.

y = 0.5 + 3x
y = 0.5 + 3•(1)
y = 0.5 + 3
y = 3.5

So, now we have another point on the graph of y = 0.5 + 3x, namely (1, 3.5).

Let's compare it to the starting point:

(0, 0.5) ----> (1, 3.5)

In other words, for every 1 unit increase in x, there must be a 3 unit increase in y because of the 3x term in the given linear function.

Answer 6

Note: the same procedure can be used for function #2, but the given function is not linear ie of the form y = mx +b.