Deck 4: Functions

Question 1

Is this relation $y= \pm \sqrt{3} x$ also a function?

Answer 1

False

Question 2

Is this relation $y=x^{2}-3 x$ also a function?

Answer 2

True

Question 3

Is the relation $y=4 \sqrt[3]{x}$ also a function?

Answer 3

True

Question 4

Is the relation $y^{2}-2 x^{2}=4$ also a function?

Question 5

Is the relation $y=|x|$ also a function?

Question 6

Is the set of ordered pairs $(0,1),(1,2),(2,3),(3,4)$ a function?

Question 7

Is the set of ordered pairs $(2,5),(3,9),(4,17),(5,5)$ a function?

Question 8

Is the set of ordered pairs $(-1,5),(-2,4),(1,6),(-1,-5)$ a function?

Question 9

Write $y$ as a function of $x$ , where $y$ is equal to half the square root of $x$ , diminished by the square of $x$ .

Question 10

Write $y$ as a function of $x$ , where $y$ equals two times $x$ squared, plus the reciprocal of $x$ .

Question 11

Write $y$ as a function of $x$ , where $y$ is a product with one factor equal to one more than $x$ and the other factor equal to double $x$ diminished by 4 .

Question 12

Write this function in literal form: $y=3-2 x^{2}$

Question 13

Write this function in literal form: $y=4 x^{3}-x^{2}$

Question 14

Write this function in literal form: $y=\frac{\sqrt{x}}{5}+1$

Question 15

Write this function in literal form: $y=\sqrt{5 x-1}$

Question 16

Write this function in literal form: $y=5 \sqrt{x-1}$

Question 17

Express the volume of a cube as a function of its side length $s$ .

Question 18

Express the surface area of a cube as a function of its side length $s$ .

Question 19

Write an equation to express the area $A$ of a square as a function of its side length $a$ .

Question 20

Gas costs $\$ 1.35 /$ L. Write an equation to express the price $P$ as a function of the number of litres of gas G.

Question 21

A car is travels at a speed of $110 \mathrm{~km} / \mathrm{h}$ . Write an equation to express the distance $d$ as a function of time $t$ .

Question 22

State the domain and range of this function:
$(5,32),(3,8),(2,4),(4,16),(1,2),(0,1)$

Question 23

State the domain and range of this function:
$(-4,-2),(-2,4),(0,3),(2,7),(4,18)$

Question 24

State the domain and range of this function:
$\begin{array}{c}x: & -1 & 0 & 1 & 3 & 5 & 10 \\y: & -2 & 4 & 6 & -1 & -2 & 17 \end{array}$

Question 25

Find the domain and range of this function: $y=\frac{3}{\sqrt{2-x}}$

Question 26

Find the domain and range of this function: $y=\frac{2}{\sqrt{x-3}}$

Question 27

Find the domain and range of this function: $y=\frac{x-3}{x+3}$

Question 28

Find the domain and range of this function: $y=\frac{x}{x-1}$

Question 29

Find the domain and range of this function: $y=\sqrt{x+1}$

Question 30

Find the domain and range of this function: $y=\sqrt{6-3 x}$

Question 31

Find the domain and range for the function: $y=\frac{1}{\sqrt{x^{2}-9}}$ .

Question 32

What is the range of the function $y=x+13$ with domain $-2 \leq x \leq 4$ ?

Question 33

Label each function as implicit or explicit. If explicit, name the dependent and independent variables.
(a) $x^{2}+y^{2}=1$
(b) $x=4 y+2$
(c) $x+2 y^{3}+4=0$
(d) $w-2 x=y$

Question 34

Label each function as implicit or explicit. If explicit, name the dependent and independent variables.
(a) $y=x^{2}+3 x$
(b) $5 x-3 y+4=0$
(c) $14 y+13=0$
(d) $y=2 x+3$

Question 35

Is this equation in implicit or explicit form? $y=3-2 x y$

Question 36

Is this equation in implicit or explicit form? $x^{2}+y^{2}=1$

Question 37

Label the dependent and independent variables in this equation: $x=w z+z^{2}$

Question 38

Label the dependent and independent variables in this equation: $c=a^{2}+b^{2}$

Question 39

If $3 y^{2}-3 x+5 y=6+x-y$ , write $x=f(y)$ .

Question 40

If $x=\frac{4}{y}+6$ , write $y=f(x)$ .

Question 41

If $a^{2}+3 b+c=40$ , write $b=f(a, c)$ .

Question 42

If $3 x-5 x^{2} y=10 x$ , write $y=f(x)$ .

Question 43

If $12 x y+\frac{2 x}{w}=3$ , write $w=f(x, y)$ .

Question 44

If $f(x)=x^{3}+7 x$ , find $f(-2)$ .

Question 45

If $f(x)=9-2 x^{2}$ , find $f(5)$ .

Question 46

If $f(x)=9+5 x-3 x^{2}$ , evaluate $f(-1.1)$ .

Question 47

If $f(x)=\frac{3}{\sqrt{x+14}}$ , calculate $f(50)$ .

Question 48

Given $f(x)=\frac{12}{x}$ , find $f(4)+f(6)-f(2)$ .

Question 49

Given $f(x)=\frac{12}{x}$ , find $f(-4)+f(-6)-f(-2)$ .

Question 50

Given $f(x)=x^{3}+5 x-3$ , find $\frac{f(3)}{f(1)+f(-1)}$

Question 51

Given $f(x)=3 x^{2}+5$ , write a simplified expression for $\frac{f(2+h)-f(2)}{h}$ .

Question 52

Given $f(x)=x^{3}$ , write a simplified expression for $\frac{f(1+h)-f(1)}{h}$ .

Question 53

If $f(x)=3 x^{2}-2 x+1$ , write an expression for $f(c)$ .

Question 54

If $f(x)=\sqrt{x-4}$ , write a simplified expression for $f(a)+f(4 a)$ .

Question 55

If $f(x)=(x+2)^{2}$ , write a simplified expression for $f(a+2)$ .

Question 56

If $f(x)=5 x^{2}-3 x-8$ , find $f(m-n)$ .

Question 57

If $g(x)=\frac{1}{2 x^{2}}$ and $h(x)=-3 x$ , find $2 h(5)-g(0.25)$ .

Question 58

If $f(x)=\frac{30}{x^{2}}$ and $g(x)=5 x-1$ , find $f(2)-g(0.1)$ .

Question 59

If $f(x)=3 x$ and $g(y)=y^{2}$ , find $f(1)+g(4)$ .

Question 60

If $f(x, z)=5 x^{2}-6+2 z$ , calculate $f(2,-5)$ .

Question 61

If $g(x, y)=9 x^{2}-4 y^{2}$ , write an expression for $g\left(2 a, a^{2}\right)$ .

Question 62

If $f(x, y, z)=z^{2}-x+5 y$ , determine the value of $f(-4,1,-3)$ .

Question 63

If $f(x, y, z)=z^{2}-x+5 y$ , determine the value of $f(4,-1,3)$ .

Question 64

If $g(x, y, z)=x^{2}+y^{3}-z$ , calculate $\frac{4 g(5,2,1)-3 g(-3,4,-1)}{2 g(1,-1,5)}$ .

Question 65

If $h(a, b, c)=a^{2}+b^{3}-c$ , evaluate $4 h(-1,0,5)+3 h(5,-3,0) \times(-2) h(1,-3,4)$ .

Question 66

The distance from a point $(x, y)$ to the point $(-2,-3)$ is given by the function $d(x, y)=\sqrt{(x+2)^{2}+(y+3)^{2}}$ . Calculate the distance from $(2,5)$ to $(-2,-3)$ to 3 significant digits.

Question 67

The temperature $\left({ }^{\circ} \mathrm{C}\right)$ at height $h$ metres over the point $(x, y)$ is given by the function $T(x, y, h)=12+$ $\frac{10}{x y+10} \frac{h}{4}$ .
(a) What is the temperature at height $3 \mathrm{~m}$ above $(6,5)$ ?
(b) What is the temperature right at the point $(6,5)$ ?

Question 68

The density $(\mathrm{g} / \mathrm{L})$ of a substance is given by the function $d(m, v)=m v^{-1}$ , where $m$ is the mass $(\mathrm{g})$ and $v$ is the volume (L). What is the density of $0.250 \mathrm{~L}$ of mercury with a mass of $0.310 \mathrm{~kg}$ ?

Question 69

The amount of interest earned at $4.25 \%$ compounded monthly is given by the function $f(P, t)=$ $P\left(1+\frac{0.0425}{12}\right)^{12 t}-P$ , where $P$ is the amount invested and $t$ is the number of years. How much will $\$ 5000$ earn in 2 years?

Question 70

Given $f(x)=2 x^{3}$ and $g(x)=x+1$ , write the composite function $g[f(x)]$ .

Question 71

Given $f(x)=3 x^{2}+x$ and $g(x)=x-10$ , write the composite function $f[g(x)]$ .

Question 72

Given $f(x)=x^{2}+1$ and $g(x)=7-x$ , calculate $f[g(-1)]$ .

Question 73

Given $f(x)=x^{2}+1$ and $g(x)=7-x$ , calculate $g[f(2)]$ .

Question 74

Given $f(x)=2 x^{3}$ and $g(x)=x+1$ , calculate $f[g(-5)]$ .

Question 75

Given $f(x)=x^{2}-5$ and $g(x)=x^{3}$ , evaluate $g[f(-1)]$ .

Question 76

Given $f(x, y)=2 x y, g(w)=w^{2}$ , and $h(z)=z+3$ , evaluate $f[g(2), h(1)]$ .

Question 77

Given $f(x)=4 x-2$ and $g(x)=\sqrt{x+2}+1$ , write the composite function $f[g(x)]$ .

Question 78

If $y=5 w+2 x^{2}, x=2+3 z$ , and $z=2 w-5$ , write $y$ as a function of $w$ .

Question 79

Write the inverse of $y=6(x-3)+2 x$ .

Question 80

Write the inverse of $y=2(x+4)-7(x-2)$ .