Question

Use the four functions below for this question: f(x) g(x) h(x) j(x) graph of line going through (negative 2, 2) and (negative 1, negative 1) g(x) = 3x − 4 Kelly had 4 apples in her kitchen on Monday. On Tuesday, only 1 was left. x j(x) −2 −2 2 10 6 22 Compare and contrast these four functions using complete sentences. Focus on the slope and y-intercept first, and then on any additional properties of each function.

Answer 1

We have four functions:

For f(x) we have two points (-2,2) and (-1,-1)

we will use two point form which is:

So, on substituting the values we get:

So, f(x)=-3x-4

We have g(x)=3x-4

Now, we will from h(x) we have two points let initial point on monday is (0,4) and tuesday (1,1) again use two point form we get:

So, h(x)= -3x+4

Now, we will form j(x) we have three points (2,10) , (-2,6) and (2,22)

We will use (-2,6) and (2,22) to find the function with two point form.

j(x)= 4x+14

To find the slope we will compare the given function with general equation which is y= mx +c; m is the slope

And to find y-intercept we will put x=0

f(x)=-3x-4

Slope is: -3

And y-intercept is: (0,-4)

g(x)=3x-4

Slope is: 3

And y-intercept is: (0,-4)

h(x)= -3x+4

Slope is: -3

And y-intercept is: (0,4)

j(x)= 4x+14

Slope is: 4

And y-intercept is: (0,14)

Answer 2

We have been given the four functions

f(x) from two points (-2,2) and (-1,-1)

Using two point formula which is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-2=(-1-2)/(-1+2)(x-(-2)`

On simplification we get:

`y=-4-3x`

`f(x)=-4-3x`

g(x) is given:

`g(x)=3x-4`

Now, for h(x) we have information Kelly had 4 apples in her kitchen that is 4x

And one was left on tuesday

So,
`h(x)=4x-3`

And for j(x) we have been given points:

(-2,-2),(2,10),(6,22)

So, again using the two point slope form to get the function:

`y+2=(10+2)/(2+2)(x+2)`

On simplification we will get:

`y=4+3x`

`j(x)=4+3x`

We need to tell the slope and y-intercept

For slope we compare the function with the general equation of line which is y=mx+c; m is slope

And for y-intercept put x=0 in the function.

For f(x)=-4-3x

slope is: -3

And y-intercept is: (0,-4)

For g(x)=3x-4

slope is: 3

And y-intercept is: (0,-4)

For h(x)=4x-3

Slope is: 4

And y-intercept is: (0,-3)

For j(x)=4+3x

Slope is: 3

And y-intercept is: (0,4)