Mid-term

Question 1

When deviding multipule devisions e.q 5/ 1/2 what should you do?

Answer 1

We first devide the denominator 1/2 which gives us 0.5 and then we divide 5/0.5 which gives us 10

Question 2

If a question asks you at what the graph crosses the x-axis at? You should answer in what form.

Answer 2

(x, y)

Question 3

When asked to answer a question about the x-intercept or y-intercept you should answe in the form OR a question about using the graphs of f and g to find (f + g)(0 or any other number)

Answer 3

The x or y NOT (x,y)
For the second question: we answer in this form but we also add the answer of f + g. If we was going to find find (f - g)(0 or any other number) we was going to subtract f - g

Question 4

A rule to remember always when substituting is

Answer 4

To always susitute to the right

Question 5

Slope-intercept

Answer 5

y=mx+b

Question 6

Point_slope intercept

Answer 6

y-y = m(x-x)

Question 7

When finding the avarage rate of an equation such as f(x)=x^2 - x + 4 what formula to use and how to solve it?

Answer 7

The formula is f(x^2) - f(x^1)/ x^2 - x^1
To solve it we use the equation (which in this case is f(x)=x^2 - x + 4) and then we solve for f(x^2) and then f(x^1) which will look like this: f(6) - f(2) / 6 - 2 = 34-6/4 = 28/4 = 7

Question 8

How to write the following= The y-value is four less than four times the x-value. AND The y-value is five incrfeased by the square of the x-value.

Answer 8

First equation: y= 4 - 4X or y = 4x - 4
Second: y=5+x^2 or y=x^2 + 5

Question 9

The NOTATION f o g called the ….. and is defined as ……

Answer 9

The compositionof the function f with g and is defined as f(g(x))

Question 10

What to do when finding a fuction domain such as 7/x^2 - 25?

Answer 10

Since the denominator x^2 - 25 should not be 0 we look for the numbers that make the denominator 0 which are in this case **-5 and 5 ** (remeber to always include the negative one with an x^2 equation)

Question 11

Find the domain of the function 1/square root of x-1

Answer 11

(1, infinity sign) and NOT [1, infinity sign) We use the [ Only if it was not in the denominator

Question 12

Find the domain of the function square root 25 - 5x

Answer 12

(- infinity, 5]
Always when the x (in this case 5x) is negative we change the sign > to <

Question 13

Find the domain of the function square root x -11 + square root x + 1

Answer 13

since square root x -11 will be [11, infinity) and square root x + 1 will be [-1, infinity) Our ANSWER will be [11, infinity) because it is bigger than [-1, infinity)

Question 14

Find the domain of the function square root x - 2 / x - 6

Answer 14

The answer will be [2,6) U (6, infinity) WHY? because the numerator contain the square root of x-2 and its answer is [2, infinty)

Question 15

How would you answer a question with (fg)(x) and a question with f o g

Answer 15

(fg)(x) means f(x) multiply by g(x) while f o g means f(g(x))

Question 16

interval notation means

Answer 16

The form (infinity, x) or (x,y]

Question 17

An inverse function means that

Answer 17

f = x and g = x

Question 18

Find an equation for f^-1(x), the inverse function.
f(x) = x + 7

Answer 18

We knoe that f(x) means y so y = x + 7
interchange the variables: x = y + 7
solve for y: x - 7 = y
Answer:y = x - 7

Question 19

How to determine whether the function has an inverse function or not.

Answer 19

Using the horizontal (-) test if they did not have multipule x-intercept the graph is inverse if they have multipule x-intercepts then the graph is noy inverse

Question 20

How to find if the fuction is increasing, decreasing, or constant

Answer 20

By looking at the graph we only use the x points to determine that so our answer will be in the form (x, x) NOT (x, x] nor (x, y)

Question 21

If the arror of the graph points up put the line looks like this \|

Answer 21

Meanse that its decreasing

Question 22

How to find the relative maximum for x in a graph

Answer 22

Look at the final point of an increasing line look at its x value and y value. The y value will be the relative maximum. Your answer will contain the x value and the y value

Question 23

How to determine whether the graph of the equation is symmetric with respect to the y-axis, the x-axis, the origin

Answer 23

y-axis: replace the x with -x if the equation stays the same it means it is symmetric
x-axis: replace y with -y
orgin: replace both

Question 24

An even function will propely look like: h(x) = 4x^2 - x^10

Answer 24

It will stay the same so h(x) = 4x^2 - x^10

Y-AXIS

Question 25

An odd function will propely look like: f(x) = x^3 + 4x

Answer 25

Both will be negative so f(x) = - x^3 - 4x

ORGIN

Question 26

A neither function will propely look like: f(x) = x^4 - 2x

Answer 26

One of them will be positive and the other will be negative so f(x) = - x^4 - 2x

NEITHER

Question 27

You round down to the nearest year even if the answer

Answer 27

even if it was 2024.6 which is a number that is bigger than 5

Question 28

In word questions, usually the equation f(x) will be

Answer 28

in the slope-interceot form and if the question asked about a decrease or increas after a perticaller year we have to add our answer to the year (e.q answer: 25.6 and year 1955 the final answer will be: 1980)

Question 29

In a word equation that have f(x) and g(x) means

Answer 29

The functions will be diffrent

Question 30

In a word equation, 90% means

Answer 30

0.9

Question 31

In a word equation, 90% means

Answer 31

0.9

Question 32

How to find the center and radius of the circle? (x-2)^2 + (y+5)^2 = 49

Answer 32

Center is (h,k) and because 2 is negative that means it is positive and the opoosite for 5 so the center is (2,-5). The radius is 7 because 49^2 = 7

Question 33

How to write the equation of the circle in standard form? x^2 + y^2 - 6x + 8y - 11 = 0

Answer 33

First we move the 11 to the other side and just leave x^2 + y^2 - 6x + 8y.
Arrange the x to be next the x and finish the equation to get the form (x-h)^2, so x^2 - 6x +9 will give us (x-3)^2 (NOTE: because we add the 9 we have to add it to the other side next to the 11) Do the same thing for the y and the center will be (3, -4) and the raduis 6 (because it was 36)

Question 34

How to find the vertex and the coordinates?

Answer 34

Using the vertex of the parapola formula to find the x-coordinate and then change the x of the equation to the answer we found to find the y-coordinate so the vertex will be (x, y)

Question 35

How to determine if a function has a minimum or maximum value?

Answer 35

If a > 0 then the parabola is going to open upwards and the minimum will be at the vertex but if a < 0 then the maximum will be at the vertex

Question 36

RANGE ISSSS

Answer 36

All the points of y in the graph where the domain is all the points of x in the graph.

Question 37

Varies directly

Answer 37

y=kx and varies jointely is the same but with two variables e.q y=kab

Question 38

Varies inversely

Answer 38

y=k/x

Question 39

A=p(1+r/n)^ni

Answer 39

p = investment
r = interest rate (if 4.25% then 0.0425)
n = compounding (if it was monthy than you put 12 if semianuual then you will put 2 if quartly you put 4 and if it is continuous then you use the other formula A=pe^rt)
t = number of years