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mhasan420
mhasan420, Master's Degree
Category: Pre-Calculus
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Experience:  BA Maths, Oxford
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Determine whether the given function is linear or nonlinear.

Customer Question

Determine whether the given function is linear or nonlinear. If it is linear determine the slope.
x y=f(x)

1 4
2 6
3 8
4 10
5 12

Determine the slope.


Could you write down how you got the answer step by step, thanks.
Submitted: 5 years ago.
Category: Pre-Calculus
Expert:  mhasan420 replied 5 years ago.
Hi there!

There are several ways to approach this problem. One simple way is to observe that when x increases by 1, f(x) always increases by 2. Since f(x) always increases by 2 when x increases by 1, it can be written in the form y = mx + c and is hence a linear function.

The slope will be the value that f(x) increases by when x increases by 1. As observed above, this is 2. Hence, the slope is 2.

Let me know if you require further clarification. If not, please click 'Accept'. Thanks! :)
mhasan420 and other Pre-Calculus Specialists are ready to help you
Customer: replied 5 years ago.
Determine whether the given function is linear or nonlinear. If it is linear determine the slope.
x y=f(x)

1 -6
2 0
3 3
4 4
5 1

Is the function a linear function?
Determine the slope.


Could you write down how you got the answer step by step, thanks.
Expert:  mhasan420 replied 5 years ago.
Hi there!

Let us look at what happens when the x value increases. As x goes from 1 to 2, the y value increases by 6. As x goes from 2 to 3, the y value increases by 3. We do not need to go further. Since the value of y increases by different values when increase the x value by 1, the function is definitely not linear.

Let me know if you require further clarification. If not, please click 'Accept'. Thanks! :)
mhasan420 and other Pre-Calculus Specialists are ready to help you
Customer: replied 5 years ago.
For the linear function f(x)=3x+6,
(a) Determine the slope and y-intercept
(b) Use the slope and y-intercept to graph the linear function.
(c) Determine the average rate of change of the function.
(d) Determine whether the linear function is increasing, decreasing, or constant.

The slop is___?
Could you write down how you got the answer step by step, thanks.
Expert:  mhasan420 replied 5 years ago.
Hi there!

a)

The slope is the coefficient of x and the y-intercept is the constant term in the function. Hence,

Slope = 3, y-intercept = 6

b)



c)

The rate of change will be equal to the slope which is 3.

d)

As the values of x increase, the value of f(x) always increases. Hence, it is an increasing function.

Hope this helps. If so, please click 'Accept'. Thanks! :)
Customer: replied 5 years ago.

I am having trouble with graphing number 1. Any suggestions or help is greatly appreciated.

1. Given the quadratic equation y = -12x^2 - 2x - 2 find:

a. Vertex (h, k).

A = -12, b = -2, c = -2

H = -b/2a = -(-2)/2(-12) = 2/-24 = -1/12

K = f(h) = -12(-1/12)^2 - 2(-1/12) - 2 = -12(1/144) + 1/6 - 2 = -1/12 + 2/12 - 24/12 = -23/12

Vertex (h, k) = (-1/12, -23/12)

b. axis of symmetry (x = h); is -1/12

c. intercepts. Y-intercept = (0, f(0)) y- intercept is (0, -2)

f(0) = -12(0)^2 - 2(0) - 2 = 0 - 0 - 2 = -2

There are NO x-intercepts

X = [-b +/- sqrt (b^2 - 4ac)]/2a = [-(-2) +/- sqrt (-2^2 - (4)(-12)(-2)]/2(-12)= [2+/- sqrt (4-96)]/-24

= (2+/- sqrt -92)/24 = (2+/- 2i*sqrt 23)/-24

d. domain all real numbers

e. range (-¥, -23/12]

f. interval where graph is increasing. (-¥, -1/12)

g. interval where graph is decreasing (-1/12, ¥)

h. graph

Expert:  mhasan420 replied 5 years ago.
Hi there!

Do you just need help with the graphing?

The way you should graph is that the first thing you should do is to mark the x and y intercepts and the vertex. If possible, draw a dotted line through the axis of symmetry and then draw an inverted parabola through those 3 points. It should look like this:



Hope this helps. It would be great if you could 'Accept' this and my previous answer. Thank you. :)

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