1.2 domain and range

Question 1

domain

Answer 1

x values. input. locaters on a graph

Question 2

range

Answer 2

y values. output. max/mins

Question 3

math moral laws

Answer 3

1- thou shalt not divide by zero
2- thou shalt not take the square root of a negative number.
3- the log of 0 does not exist

Question 4

set notation

Answer 4

{ } curly brackets. when the domain and/or range are distinct numbers/ data and NOT an interval of values. Set number.

D:{2, 3,4,5}
R:{6,8,10}

Question 5

closed intervals

Answer 5

brackets. describes intervals that do not include end points. point of a curve. Also called inclusive

Question 6

interval notation

Answer 6

use parenthesis (). Continuous curves. Open dot.

Question 7

what are the x values of a parabola?

Answer 7

zeros/roots/solutions/x-intercepts

Question 8

how do you find the vertex for a parabola? y=ax^2+bx+c

Answer 8

-b/2a

Question 9

what does the symbol E stand for?

Answer 9

is a member of. tells you what kind of value an interval describes

Question 10

Inclusive

Answer 10

[ ] point on a curve. Solid dot.

Question 11

True or false: is infinity inclusive?

Answer 11

No, because it cannot be bound. Infinity + 1!

Use ( )

Question 12

Graph. x=4 domain and range.

Answer 12

Not a function. Vertical line.
D: {4}
R: (-inf, inf)

Question 13

Graph y= -5. D and r.

Answer 13

Not a function. Horizontal line.
D: (-inf, inf)
R: {-5}

Question 14

Graph y=3x +2. D and r.

Answer 14

Yes a function. Linear. Both domain and range are (-inf, inf)

Question 15

Graph x^2 -5x+6. D and r.

Answer 15

Parabola. ax^2 + bx + c.
Yes function. Graph: find vertex. x= -b/2a. Plug x back into the function to find the y point. (x,y) is the vertex.
D: (-inf,inf)
R: [vertex, inf)

Note that it’s inclusive because the vertex is a point on the curve.

Question 16

Graph 1/(x+2) domain

Answer 16

Graph has two curves. Parent function is y=1/x.
One in the first quadrant and one in the thirst quadrant. Asymptote at (0,0).

Math moral law says we can’t divide by zero. So to find domain,
SET DENOM = 0.

x+2=0.
x=-2.

D: (-inf,-2) U (-2,inf)

Question 17

Graph y= √(3-4x) domain

Answer 17

Parent function: y=√x. Graph is a teacup.
Has a vertical rotation because of the -.
Math moral law says that we can’t take the square root of a negative number. Why? Because it’s imaginary.

Finding domain: SET GUTS ≥ 0.
3-4x≥0.
3≥4x

X≤3/4

D: (-∞, 3/4]

Question 18

Graph log base 4 (x-5). And domain

Answer 18

Parent function: logs start at (1,0)
Graph will have an asymptote at (5,0) and a point on (6,0) with a continuous curve.

Math moral law says that log of 0 does not exist. Why? Because you can’t raise a number to a power that will equal 0. Logs and exponentials are inverses, so likewise, you cannot take the log of zero and get a number.

Finding domain: SET GUTS >0.

x-5>0
x>5.

D: (5,∞)
R: (-∞,∞)

Question 19

Graph y=5sin2x and d and r

Answer 19

Sin waves are periodic. Starts at center line. Amplitude is 5. λ= 2π/b