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Use the four functions below for this question:



f(x)

g(x)

h(x)

j(x)

graph of line going through (– 2, 2) and (– 1, – 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.

Verified Answer :

HomertheGenius

We will solve the system:
2 = - 2 m + b
-1 = - m + b / ·(-1 )
--------------------------
2 = - 2 m + b
+
1 = m - b
-----------------
3 = -m,   m= -3,    2 = 6 + b,   b = -4,
f ( x ) = - 3 x - 4
For the linear function h (x)9 we have 3 apples less every day:
h ( x) = - 3 x + 4
- 2 = - 2 m + b
+
10 = 2 m + b
-------------------
8 = 2 b,             b = 4,  m = 3
j ( x ) = 3 x + 4

Four linear functions are:
1 ) f ( x ) = - 3 x - 4 
Linear function has a slope: m = -3, y-intercept: y = -4, zero: x = -4/3 and this function is constantly decreasing.
2 ) g (x ) = 3 x - 4
Function has a slope: m = 3, y-intercept : y =-4, zero: x = 4/3 and it is constantly increasing.
3 ) h ( x ) = - 3 x + 4
Function has a slope: m = -3, y-intercept: y = 4, zero: x = 4/3 and it is constantly decreasing.
4 ) j (x) = 3 x + 4
Function has a slope m = 3, y-intercept : y = 4, zero: x = 4 and it is constantly increasing.
Two linear functions f ( x ) and h ( x ) are parallel ( have an equal slope ), and  also are g ( x ) and j ( x ).   

Answer:

We have four functions:

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

we will use two point form which is:

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

So, on substituting the values we get:

\(y-2=\frac{-1-2}{-1-(-2)}(x-(-2))\)

\(y-2=\frac{-3}{x+2}\)

\(y=-3x-4\)

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:

\(y-4=-3(x-0)\)

\(\Rightarrow y=-3x+4\)

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.

\(y-6=\frac{22-6}{2+2}x+2)\)

\(\Rightarrow y=4x+14\)

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)

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