Question

f(x)
g(x)
h(x)
j(x)
Jesse got $5 from his dad and he makes $2 each time he walks the neighbor's dog.
x

g(x)

–2

–1

2

–9

6

–17

a line going through the point (0, 5) and the point (3, negative 1)
j(x) = 2x – 5


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

Answer:

 

Step-by-step explanation:

We will define the functions as:

f(x)=5+2x from the given information:

Now we have three points: (-2,-9) ,(-1,6) and (2,-17)

We will use two point form to find g(x)

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

We will use the point (-2,-9) and (-1,6) on substituting the values in the above formula we get:

$y-(-9)=\frac{6+9}{-1+2}(x+2)$

On simplification we get:

$y=-15x-39$

$g(x)=-15x-39$

Now, we will form h(x) from the points (0,5) and (3,-1) with the two point form:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-5=\frac{-1-5}{3-0}(x-0)$

On simplification we will get:

$y=-2x+5$

$h(x)=-2x+5$

Now, we have j(x)=2x-5

We will compare the function with general equation y= mx+c; m is slope of line.

And to find y-intercept put x =0 in the given function.

The slope of f(x)=5+2x  is 2 because 2 is coefficient of x which is m

And y-intercept is:  (0,5).

g(x)=-15x-39

Slope of g(x) is -15

And y-intercept is: (0,-39).

h(x)=-2x+5

Slope of h(x) is: -2

And y-intercept is: (0,5)

j(x)=2x-5

Slope of j(x) is: 2

And y-intercept is: (0,-5).