Assignment 1

Investigation 2

Make up linear functions f(x) and g(x). Explore, with different pairs of f(x) and g(x) the graphs for

i. h(x) = f(x) + g(x)

ii. h(x) = f(x).g(x)

iii. h(x) = f(x)/g(x)

iv. h(x) = f(g(x))

Summarize and illustrate.

So choosing f(x)= x²+5

and g(x)=2x+17

We get

(i) h(x)=f(x)+g(x)=(x²+5)+(2x+17)

(ii.) h(x)=f(x)×g(x)= (x²+5)×(2x+17)

(iii.) h(x)=f(x)/g(x) )= (x²+5)/(2x+17)

(iv.) h(x)=f(g(x)) )= ((2x+17)²+5)

To make this easier to see let’s put all the graphs together

You can see the progression into becoming a straight line. Starting from f(x) and going to g(x) with the different operations.

Now, let’s choose different values of f(x) and g(x) and observe what happens.

Let’s take f(x)=x⁴+5x+10

and g(x)=sin(x)+x²+3

Now we get

(i.) h(x)=f(x)+g(x)=(x⁴+5x+10)+(sin(x)+x²+3)

(ii.) h(x)=f(x)×g(x) =(x⁴+5x+10)×(sin(x)+x²+3)

(iii.) h(x)=f(x)/g(x)=(x⁴+5x+10)/(sin(x)+x²+3)

(iv.) h(x)=f(g(x))= ((sin(x)+x²+3)⁴+5x+10)

Now, let’s put them all on the same graph so that it is easier to make an observation

Again, you can notice the same general progression. Clearly these operations merely change the position of the graph along the y-axis, but not it’s shape until division comes into play.

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