Deck 5: Graphs

Question 1

In which quadrant does each point lie?
(a) $(3,-4)$
(b) $(1,5)$
(c) $(-2,-2)$

Answer 1

(a) fourth
(b) first
(c) third

Question 2

If $a$ and $b$ are positive quantities, in which quadrant would $(-a,-b)$ lie?

Answer 2

third

Question 3

If $a$ and $b$ are positive quantities, in which quadrant would $(a,-b)$ lie?

Answer 3

fourth

Question 4

In which quadrants is the abscissa negative?

Question 5

In which quadrants is the ordinate positive?

Question 6

In which quadrant is the ordinate negative and the abscissa positive?

Question 7

If $(a, b)$ is in the first quadrant, in which quadrant is $(-a,-b)$ ?

Question 8

If $(a, b)$ is in the second quadrant, in which quadrant is $(-a,-b)$ ?

Question 9

Find the ordinate of any point on a horizontal straight line that passes through the point $(3,-1)$ .

Question 10

Find the abscissa of any point on a vertical straight line that passes through the point $(-4,9)$ .

Question 11

Graph the points $(1,1),(5,1),(2,2),(6,2)$ , connect them, and identify the geometric figure formed.

Question 12

Graph the points $(-5,10),(0,0),(3,12),(8,2)$ , connect them, and identify the geometric figure formed.

Question 13

Graph the points $(-5,5),(-1,1),(-3,-1)$ , connect them, and identify the geometric figure formed.

Question 14

Graph these points, and connect them with the curve that fits the data: $(-3,21),(-2,10),(-1,3),(0,0)$ , $(1,1),(2,6),(3,15)$

Question 15

Graph these points, and connect them with the curve that fits the data: $(1,1),(2,2),(3,4),(4,6),(5,9)$

Question 16

Graph the straight line $y=-2 x+6$ by plotting two points, plus a third as a check.

Question 17

Graph the straight line $y=3 x-4$ by plotting two points, plus a third as a check.

Question 18

Graph the straight line $y=-2 x-4$ by plotting two points, plus a third as a check.

Question 19

Graph $y=x^{2}+3 x$ by plotting points for integer values of $x$ from -3 to 3 and connecting them with a smooth curve.

Question 20

Graph $y=x^{3}-4 x^{2}-1$ by plotting points for integer values of $x$ from -3 to 3 and connecting them with a smooth curve.

Question 21

Graph $y=3 x^{4}-1$ by plotting points for integer values of $x$ from -2 to 2 and connecting them with a smooth curve.

Question 22

Graph $y=x^{3}+3 x^{2}-5$ by plotting points for integer values of $x$ from -3 to 3 and connecting them with a smooth curve.

Question 23

Graph $y=2 x^{3}-3 x$ by plotting points for integer values of $x$ from -3 to 3 and connecting them with a smooth curve.

Question 24

Graph $y=x^{4}+25$ by plotting points in 0.5 intervals of $x$ from -2 to 2 and connecting them with a smooth curve.

Question 25

Calculate the slope of a straight line with rise $=-5$ and run $=-4$ .

Question 26

Calculate the slope of a straight line with rise $=35$ and run $=-5$ .

Question 27

Calculate the slope of a straight line with rise $=-3$ and run $=4$ .

Question 28

Calculate the slope of a straight line with rise $=10$ and run $=3$ .

Question 29

Calculate the slope of the straight line connecting $(-1,7)$ and $(4,-2)$ .

Question 30

Calculate the slope of the straight line connecting $(5,-4)$ and $(-1,-3)$ .

Question 31

Calculate the slope of the straight line connecting $(5,-3)$ and $(5,-4)$ .

Question 32

Calculate the slope of the straight line connecting $(4,-5)$ and $(6,-5)$ .

Question 33

Calculate the slope of the straight line connecting $(-12,-1)$ and $(-6,-7)$ .

Question 34

Calculate the slope of the straight line connecting $(2,-6)$ and $(-6,10)$ .

Question 35

A straight line has slope $=3$ and $y$ -intercept $=-4$ . Write its equation in slope-intercept form and make a graph.

Question 36

A straight line has slope $=-\frac{1}{3}$ and $y$ -intercept $=5$ . Write its equation in slope-intercept form and make a graph.

Question 37

A straight line has slope $=0.8$ and $y$ -intercept $=-1.2$ . Write its equation in slope-intercept form and make a graph.

Question 38

A straight line has slope $=-10$ and $y$ -intercept $=-4$ . Write its equation in slope-intercept form and make a graph.

Question 39

Determine the slope and $y$ -intercept for $y=\frac{1}{3} x+1$ , and make a graph.

Question 40

Determine the slope and $y$ -intercept for $y=\frac{-3}{4} x-\frac{1}{2}$ , and make a graph.

Question 41

Determine the slope and $y$ -intercept for $y=3 x-6$ , and make a graph.

Question 42

Determine the slope and $y$ -intercept for $3 x-4 y=6$ , and make a graph.

Question 43

Determine the slope and $y$ -intercept for $6 x-y=4$ and make a graph.

Question 44

Plot $y=3 x^{2}-5 x+1$ using a graphing calculator or software. Use the TRACE key, or the equivalent software tool, to locate the $x$ -intercepts and the maximum or minimum point.

Question 45

Plot $y=-5 x^{2}-10 x+4$ using a graphing calculator or software. Use the TRACE key, or the equivalent software tool, to locate the $x$ -intercepts and the maximum or minimum point.

Question 46

This data shows the temperature and vapour pressure for liquid nitric acid. Plot the data, being sure to label your graph completely:
$\begin{array}{l|llllll}Temperature \left({ }^{\circ} \mathrm{C}\right) & 0 & 10 & 20 & 30 & 40 & 50 \\Vapour Pressure \mathrm{mm} \mathrm{Hg}) & 14.4 & 26.6 & 47. & 81.3 & 133 & 208 \end{array}$

Question 47

This data shows the melting point $T$ and the percent of lead $P$ for a certain alloy. Plot the data, being sure to label your graph completely:
$\begin{array}{l|llllll}Percent Lead P(\%) & 14.4 & 26.6 & 47. & 81.3 & 133 & 208 \\Melting Point T\left({ }^{\circ} \mathrm{C}\right) & 0 & 10 & 20 & 30 & 40 & 50\end{array}$

Question 48

This data shows the estimated weight per inch of length for round steel shafting used for noise reduction. Plot the data, being sure to label your graph completely:

Question 49

The pressure of a gas is given by $P=\frac{1400}{V}$ where $V$ is the volume. Plot $P$ (in. $\mathrm{Hg}$ ) for values of $V$ from 10 to 50 cubic inches.

Question 50

A milling machine has a purchase price $P$ of $\$ 24,000$ and an annual depreciation $A$ of $\$ 1,200$ . Graph the value of the machine $y$ at the end of each year for $t=10$ years, using the equation $y=P-A t$ .

Question 51

Thermistors are used in electrical circuits to determine changes in temperature based on changes in the resistance. Plot this experimental data, being sure to label your graph completely:
$\begin{array}{l|lllll}Resistance (\Omega) & 340.0 & 451.1 & 636.0 & 911.3 & 1101.0 \\Temperature \left({ }^{\circ} \mathrm{C}\right) & 57.625 & 50.128 & 40.120 & 30.131 & 25.113 \end{array}$

Question 52

Plot the parametric equations $x=t^{2}$ and $y=2 t-1$ for $t$ between -3 and 3 .

Question 53

Plot the parametric equations $x=3 t+2$ and $y=t^{2}$ for $t$ between -3 and 3 .

Question 54

Plot the parametric equations $x=\sqrt{t^{2}+1}$ and $y=t^{2}$ for $t$ between -3 and 3 .

Question 55

Plot the parametric equations $x=1 /(t+4)$ and $y=t^{2}$ for $t$ between -3 and 3 .

Question 56

Plot the parametric equations $x=\sqrt{2 t^{2}+5}$ and $y=t$ for $t$ between -3 and 3 .

Question 57

The equation $x^{3}-4 x^{2}-3=0$ has at least one root between $x=-10$ and $x=10$ . Graph the equation to find the approximate value of the root(s).

Question 58

The equation $2.5 x^{2}-14=0$ has at least one root between $x=-10$ and $x=10$ . Graph the equation to find the approximate value of the root(s).

Question 59

The equation $(x-1)^{2}=3 x+2 x^{2}$ has at least one root between $x=-10$ and $x=10$ . Rewrite the equation, then graph it to find the approximate value of the root(s).

Question 60

Graph these functions to estimate the coordinates of the intersection point: $3 x+2 y=12, x-4 y=8$

Question 61

Graph these functions to estimate the coordinates of the intersection point: $3 x-5 y=10, x+y=5$

Question 62

Graph these functions to estimate the coordinates of the intersection point: $y=2 x^{2},-4 x+y=-2$

Question 63

Graph these functions to estimate the coordinates of the intersection point: $y=2 x^{3}, x^{2}+y=-2$

Question 64

Graph these functions to estimate the coordinates of the intersection points: $y=x^{2}, y=2$