Question

Use the four functions below for this 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


please help and answer

Answer 1

f (x ) = 2 x + 5
For g (x) we will solve the system:
- 1 =-2 m + b
+
-9 = 2 m + b
----------------------
-10 = 2 b,  b = -5
-9 = 2 m - 5
2 m = -4
m = -2
g ( x ) = - 2 x - 5
For h (X):
m = (-1-5 ) / ( 3-0 ) = -6/3 = -2
5 = 0 + b,   b = 5
h ( x) = - 2 x + 5.
Now we have 4 linear functions:
1 ) f ( x ) = 2 x + 5
The slope is m = 2, y - intercept: y = 5 , zero: x = -2.5 and the function increases ( m > 0 ).
2 ) g(x) = - 2 x - 5
The slope is m = - 2, y-intercept: y =-5 , zero: x = -2.5 and the function decreases ( m < 0 ).
3 ) h ( x ) = - 2 x + 5
The slope is m = - 2, y - intercept . y = 5, zero: x = 2.5 and the function decreases.
4 ) j (x) = 2 x + 5
The slope is m = 2, y -intercept: y = 5, zero: x = -2.5 and the function decreases.
The functions f( x ) and j ( x ) are parallel and also g( x ) and h ( x ). They have the same slope.  
The functions f ( x ) and j (x ) are increasing and h ( x ) and h ( x ) are decreasing.