Quiz about Generral Mathematics: Functions and Relations

Question 1

What do we call the inputs of functions or the elements of $$x$$ ?

Accepted Answer

domain

Answer

relation

Answer

range

Answer

abscissa

Question 2

What do we call the outputs of functions or elements of $$y$$ ?

Accepted Answer

range

Answer

domain

Answer

relation

Answer

ordinate

Question 3

Out of the following, which one is not a function?

Accepted Answer

$$\left\{(0,\ 2),\ (1,\ 3),\ (4,\ 3),\ (1,\ 2)\right\}$$

Answer

$$\left\{(0,\ 1),\ (1,\ 2),\ (2,\ 3),\ (3,\ 4)\right\}$$

Answer

$$\left\{(1,\ 3),\ (4,\ 2),\ (2,\ 0),\ (3,\ 4)\right\}$$

Answer

$$\left\{\left(1,\ 2\right),\ \left(2,\ 2\right),\ \left(3,\ 2\right),\ \left(4,\ 2\right)\right\}$$

Question 4

Which of the $$x$$ and $$y$$ values is an independent variable?

Accepted Answer

$$x$$ variable

Answer

$$y$$ variable

Answer

$$x$$ and $$y$$ variable

Answer

none of them

Question 5

An exponent which $$b$$ must have to produce $$y$$ .

Accepted Answer

logarithm

Answer

Inverse function

Answer

one-to-one function

Answer

Exponential growth

Question 6

It is used to determine if the graph is one to one function or not.

Accepted Answer

Horizontal line test.

Answer

Relation

Answer

Inverse function

Answer

Logarithm

Question 7

A straight line associated with a curve such that as a point moves along an infinite branch of the curve, the distance from point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.

Accepted Answer

Asymptote

Answer

y-intercepts

Answer

x-intercepts

Answer

horizontal line test

Question 8

Is a set of ordered pairs.

Accepted Answer

Relation

Answer

Function

Answer

Domain

Answer

Range

Question 9

It is composed of rational expressions combined with a $$\le$$ , $$\ge$$ , $$<$$ , or $$>$$ sign.

Accepted Answer

Rational Inequality

Answer

Function

Answer

Rational equation

Answer

Logarithm

Question 10

A function defined by multiple subfunctions, where each sub function applies to a certain interval of the main function's domain.

Accepted Answer

piecewise function

Answer

Linear function

Answer

Identity function

Answer

Constant function

Question 11

$$\frac{2}{x}=\frac{9}{x-3}$$

Accepted Answer

rational equation

Answer

rational expression

Answer

rational inequality

Answer

rational function

Question 12

$$\frac{1}{2x+5}$$

Accepted Answer

rational expression

Answer

rational equation

Answer

rational inequality

Answer

rational function

Question 13

$$f\left(x\right)=\frac{1}{x-2}$$

Accepted Answer

rational function

Answer

rational expression

Answer

rational equation

Answer

rational inequality

Question 14

$$2>\frac{9}{x-3}$$

Accepted Answer

rational inequality

Answer

rational expression

Answer

rational equation

Answer

rational function

Question 15

$$\frac{2}{7}>\frac{\sqrt[]{5x+1}}{x-3}$$

Accepted Answer

rational inequality

Answer

rational expression

Answer

rational equation

Answer

rational function

Question 16

$$\frac{1}{2x+5}=\frac{3}{x+5}$$

Accepted Answer

rational equation

Answer

rational expression

Answer

rational inequality

Answer

rational function

Question 17

$$\frac{2x-1}{3x+2}<12$$

Accepted Answer

rational inequality

Answer

rational expression

Answer

rational equation

Answer

rational function

Question 18

$$y=\frac{1}{x-2}$$

Accepted Answer

rational function

Answer

rational expression

Answer

rational equation

Answer

rational inequality

Question 19

$$\frac{2}{3x}+\frac{3}{4}=\frac{1}{x}$$

Accepted Answer

rational equation

Answer

rational expression

Answer

rational inequality

Answer

rational function

Question 20

$$x^2+x+1$$

Accepted Answer

rational expression

Answer

rational equation

Answer

rational inequality

Answer

rational function

Question 21

Find the value of $$y$$ in $$y=\frac{1}{x-1}$$ if $$x=-2$$ .

Accepted Answer

$$-\frac{1}{3}$$

Answer

$$\frac{1}{-1}$$

Answer

$$-1$$

Answer

$$-\frac{1}{2}$$

Question 22

Find the value of $$y$$ in $$y=\frac{1}{x-1}$$ if $$x=-1$$ .

Accepted Answer

$$-\frac{1}{2}$$

Answer

$$-\frac{1}{3}$$

Answer

$$\frac{1}{-1}$$

Answer

$$-1$$

Question 23

Find the value of $$y$$ in $$y=\frac{1}{x-1}$$ if $$x=0$$ .

Accepted Answer

$$-1$$

Answer

$$-\frac{1}{3}$$

Answer

$$undefined$$

Answer

$$-\frac{1}{2}$$

Question 24

Find the value of $$y$$ in $$y=\frac{1}{x-1}$$ if $$x=2$$ .

Accepted Answer

$$1$$

Answer

$$-\frac{1}{3}$$

Answer

$$undefined$$

Answer

$$-\frac{1}{2}$$

Question 25

Find the value of $$y$$ in $$y=\frac{1}{x-1}$$ if $$x=3$$ .

Accepted Answer

$$\frac{1}{2}$$

Answer

$$-\frac{1}{3}$$

Answer

$$undefined$$

Answer

$$1$$

Question 26

Find the value of $$y$$ in $$y=\frac{1}{x-1}$$ if $$x=4$$ .

Accepted Answer

$$\frac{1}{3}$$

Answer

$$undefined$$

Answer

$$1$$

Answer

$$\frac{1}{2}$$

Question 27

Write $$3^4=81$$ into its logarithmic form.

Accepted Answer

$$\log_381=4$$

Answer

$$\log_{81}3=4$$

Answer

$$\log_481=3$$

Answer

$$\log_34=81$$

Question 28

Write $$8^y=300$$ into its logarithmic form.

Accepted Answer

$$\log_8300=y$$

Answer

$$\log_y300=8$$

Answer

$$\log_8y=300$$

Answer

$$\log_{300}8=y$$

Question 29

Write $$\log_327=x$$ into its exponential form.

Accepted Answer

$$3^x=27$$

Answer

$$3^{27}=x$$

Answer

$$x=3^{27}$$

Answer

$$x=27^3$$

Question 30

Write $$\log_24=x$$ into its exponential form.

Accepted Answer

$$2^x=4$$

Answer

$$2^4=x$$

Answer

$$x=4^2$$

Answer

$$x^2=4$$

Question 31

Given: $$f(x)=3x+4$$ ; $$g(x)=2x-1$$

Find $$f+g$$ and determine the domain of the function.

Accepted Answer

$$\left(f+g\right)\left(x\right)=5x+3$$ $$D=\left(-\infty,\ +\infty\right)$$

Answer

$$\left(f+g\right)\left(x\right)=5x+3$$ $$D=\left[-\frac{3}{5},\ +\infty\right)$$

Answer

$$\left(f+g ight)\left(x ight)=5x+3$$

$$D=\left\{x e-\frac{3}{5} ight\}$$

Answer

$$\left(f+g ight)\left(x ight)=5x+3$$ $$D=\left\{x e-3 ight\}$$

Question 32

Given: $$f(x)=3x+4$$ ; $$g(x)=2x-1$$

Find $$f-g$$ and determine the domain of the function.

Accepted Answer

$$\left(f-g\right)\left(x\right)=x+5$$ $$D=\left(-\infty,\ +\infty\right)$$

Answer

$$\left(f-g\right)\left(x\right)=x+5$$ $$D=\left[-5,\ +\infty\right)$$

Answer

$$\left(f-g ight)\left(x ight)=x+5$$

$$D=\left\{x e-5 ight\}$$

Answer

$$\left(f-g ight)\left(x ight)=x+5$$ $$D=\left\{x e0 ight\}$$

Question 33

Given: $$f(x)=3x+4$$ ; $$g(x)=2x-1$$

Find $$fg$$ and determine the domain of the function.

Accepted Answer

$$\left(fg\right)\left(x\right)=6x^2+5x-4$$ $$D=\left(-\infty,\ -\frac{4}{3}\right]\cup\left[\frac{1}{2},\ +\infty\right)$$

Answer

$$\left(fg ight)\left(x ight)=6x^2+5x-4$$

$$D=\left\{x e-6 ight\}$$

Answer

$$\left(fg\right)\left(x\right)=6x^2+5x-4$$ $$D=\left(-\infty,\ +\infty\right)$$

Answer

$$\left(fg ight)\left(x ight)=6x^2+5x-4$$ $$D=\left\{x e4 ight\}$$

Question 34

Given: $$f(x)=3x+4$$ ; $$g(x)=2x-1$$

Find $$\frac{f}{g}$$ and determine the domain of the function.

Accepted Answer

$$\left(\frac{f}{g} ight)\left(x ight)=\frac{3x+4}{2x-1}$$ $$D=\left\{x e0.5 ight\}$$

Answer

$$\left(\frac{f}{g}\right)\left(x\right)=\frac{3x+4}{2x-1}$$ $$D=\left(-\infty,\ -\frac{4}{3}\right]\cup\left[\frac{1}{2},\ +\infty\right)$$

Answer

$$\left(\frac{f}{g} ight)\left(x ight)=\frac{3x+4}{2x-1}$$

$$D=\left\{x e1 ight\}$$

Answer

$$\left(\frac{f}{g}\right)\left(x\right)=\frac{3x+4}{2x-1}$$ $$D=\left(-\infty,\ +\infty\right)$$

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