Practice Doing Functions in Math

In mathematics, function is nothing but depending on the input value, the output value to be determined. We can map the variables of the function into a coordinate system. Function is denoted in the form of y = f(x). If a function contains only one variable then it is called as one variable function. For example: f(x) = 12x + 4. Here, x is a variable. Now, we are going to discuss some of the problems for doing functions in math.


Example Problems- Practice Doing Functions Math:

Example problem 1:

Find the ordered pairs of the function: f(x) = 10x + 2

Solution:

f(x)= 10x + 2

Substitute x=0

f (0) =  10(0) + 2

y = 2

Therefore the ordered pair (x, f(0)) is (0, 2).

Substitute x = 1

f(1) = 10(1) + 2

y = 12

Therefore the ordered pair (x, f(1)) is (1, 12).

Substitute x=2

f(2) = 10(2) + 2

y = 22

Therefore the ordered pair (x, f(2)) is (2, 22).

Substitute x=3

f(3) = 10(3) + 2

y = 32

Therefore the ordered pair (x, f(3)) is (3, 32).

The ordered pairs of the function f(x) = 10x + 2 is (0, 2), (1, 12), (2, 22), (3, 32).

Example problem 2:

Find whether the relation {(-2, 4), (-1, 6), (-1, 8), (0, 10)} is a function?

Solution:

The given ordered pair is {(-2, 4), (-1, 6), (-1, 8), (0, 10)}.

Functions / relations

Here, more than one ordered pair with the same x coordinate, but with different y coordinates. The ordered pairs (-1, 6) and (-1, 8) have the same x coordinate and y coordinates are different (i.e.,) two y coordinate 6 and 8 corresponds to a single x coordinate -1. Therefore, this relation cannot be a function.

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Additional Problems- Practice Doing Functions Math:

Example problem 3:

Find the zeros of the one variable function f(x) = x2 - 173x + 172.

Solution:

Set the equation equal to zero.

0 = x2 -173 x + 172

Factor the quadratic function and solve for x.

Here, a = coefficient of x2 = 1

b = coefficient of x = -173

c = constant term = 172

We find a × c = 1× 172 = 172 = -1*-172, (-1) + (-172) = -173 = b.

x2 - 173x + 172 = 0

x2 + (- 1 - 172)x + 162 = 0

x2 – 1 x – 172 x + 172 = 0

x (x - 1) – 172 (x - 1) = 0

 (x – 1) (x – 172) = 0

x = 1, 172

So, the zeros occur when x equals 1 and 172.

Example problem 4:

Is the function f(x) = 10x + x3 even function or odd function?

Solution:

f(x) = 10x + x3

Substitute the value –x in the place of x.

f(-x) = 10(-x) + (-x)3

f(-x) = -10x – x3 = -(10x + x3)

f(-x) = -f(x)

So, the given function f(x) = 10x+ x3 is an odd function.


Practice Problems for Doing Functions in Math:

1) Find the zeros of the one variable function f(x) = x2 - 172x + 171. (Answer: 1, 171).

2) Is the function f(x) = 2x2 + x4 even function or odd function? (Answer: even function).