Calculus Final Review Common Functions

Question 1

y=x^2

Answer 1

An upward “u”

Question 1

y=x^2

Answer 1

An upward “u”

Question 2

x=y^2

Answer 2

A sideways “u”

Question 2

x=y^2

Answer 2

A sideways “u”

Question 3

y=x^3

Answer 3

1/2(downward “u”), then 1/2 ( upward “u”)

Question 3

y=x^3

Answer 3

1/2(downward “u”), then 1/2 ( upward “u”)

Question 4

y=x^1/3

Answer 4

Previous; sideways and rotated

Question 4

y=x^1/3

Answer 4

Previous; sideways and rotated

Question 5

y=x

Answer 5

Straight diagonal line

Question 5

y=x

Answer 5

Straight diagonal line

Question 6

y=1/x

Answer 6

Opposing curves against “x” and “Y”

Question 6

y=1/x

Answer 6

Opposing curves against “x” and “Y”

Question 7

y=1/x^2

Answer 7

From x backwards up to y

Question 7

y=1/x^2

Answer 7

From x backwards up to y

Question 8

y=[x]

Answer 8

Upward “v”

Question 8

y=[x]

Answer 8

Upward “v”

Question 9

y=[x]/x

Answer 9

Open circles, then constant y=some # x

Question 9

y=[x]/x

Answer 9

Open circles, then constant y=some # x

Question 10

y=(a^2-x^2)^1/2

Answer 10

Semicircle

Question 10

y=(a^2-x^2)^1/2

Answer 10

Semicircle

Question 11

y=-f(x)

Answer 11

Reflects the graph over the x-axis

Question 11

y=-f(x)

Answer 11

Reflects the graph over the x-axis

Question 12

y=f(-x)

Answer 12

Reflects the graph over the y-axis

Question 12

y=f(-x)

Answer 12

Reflects the graph over the y-axis

Question 13

y=f(x)+c

Answer 13

Translates the graph of y=f(x) up c units

Question 13

y=f(x)+c

Answer 13

Translates the graph of y=f(x) up c units

Question 14

y=f(x)-c

Answer 14

Translates the graph of y=f(x) down c units

Question 14

y=f(x)-c

Answer 14

Translates the graph of y=f(x) down c units

Question 15

y=f(x+c)

Answer 15

Translates the graph of y=f(x) left c units

Question 15

y=f(x+c)

Answer 15

Translates the graph of y=f(x) left c units

Question 16

y=f(x-c)

Answer 16

Translates the graph of y=f(x) right c units

Question 16

y=f(x-c)

Answer 16

Translates the graph of y=f(x) right c units

Question 17

y=cf(x)

Answer 17

The graph of y=f(x) scaled vertically by c (c>0)

Question 17

y=cf(x)

Answer 17

The graph of y=f(x) scaled vertically by c (c>0)

Question 18

A plane curve is symmetric about the ---if replacing --- by ---- in its equation produces and equivalent equation.

Answer 18

y-axis, x, -x,

Question 18

A plane curve is symmetric about the ---if replacing --- by ---- in its equation produces and equivalent equation.

Answer 18

y-axis, x, -x,

Question 19

A plane curve is symmetric about ------- if replacing ---- by ---- and ---- by ---- in its equation produces and equivalent equation.

Answer 19

the origin, x, -x, y, -y

Question 19

A plane curve is symmetric about ------- if replacing ---- by ---- and ---- by ---- in its equation produces and equivalent equation.

Answer 19

the origin, x, -x, y, -y

Question 20

m=(y_2-y_1)/(x_2-x_1)

Answer 20

Slope

Question 20

m=(y_2-y_1)/(x_2-x_1)

Answer 20

Slope

Question 21

y-y_1=m(x-x_1)

Answer 21

Point-slope form

Question 21

y-y_1=m(x-x_1)

Answer 21

Point-slope form