Pre-Calculus

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Pre-Calculus

# Determine whether the given function is linear or nonlinear.

Customer Question
If it is linear determine...
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
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3/13/2012
Tutor: mhasan420, Master's Degree replied 5 years ago
mhasan420, Master's Degree
Category: Pre-Calculus
Satisfied Customers: 1,849
Experience: BA Maths, Oxford
Verified
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, Master's Degree
Category: Pre-Calculus
Satisfied Customers: 1,849
Experience: BA Maths, Oxford
Verified
Customer reply 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.
Tutor: mhasan420, Master's Degree 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, Master's Degree
Category: Pre-Calculus
Satisfied Customers: 1,849
Experience: BA Maths, Oxford
Verified
Customer reply 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.
Tutor: mhasan420, Master's Degree 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 reply 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

Tutor: mhasan420, Master's Degree 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. :)
mhasan420, Master's Degree
Category: Pre-Calculus
Satisfied Customers: 1,849
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Experience: BA Maths, Oxford

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