Question

F(x)

Answer 1

F(x) = 5 + 2x  where x is the number of times he walks the neighbours dog
y-intercept is at y=5 and slope = 2

g(x) :-  As x increases by 4 g(x) decreases by -8  so the slope is -8/4 =  -2
when x = 0, g(x)  = the y intercept  is at -1 + (-8/2) = - 5
so equation of g(x) is  g(x) = -5 -2x
h(x):-    the slope is  (3 - 5) / (1 - 0)      [  difference in y values / diff in x values]
slope = -2
so we have h(x) = -2x + c   where c = the y-intercept
when x = 0  h(x) = 5
so  c = 5
 h(x) = 5 - 2x   

  Now j(x)= 2x - 5   - slope is 2 and y intercept = -5

Answer 2

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).