Mid-term Flashcards
When deviding multipule devisions e.q 5/ 1/2 what should you do?
We first devide the denominator 1/2 which gives us 0.5 and then we divide 5/0.5 which gives us 10
If a question asks you at what the graph crosses the x-axis at? You should answer in what form.
(x, y)
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)
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
A rule to remember always when substituting is
To always susitute to the right
Slope-intercept
y=mx+b
Point_slope intercept
y-y = m(x-x)
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?
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
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.
First equation: y= 4 - 4X or y = 4x - 4
Second: y=5+x^2 or y=x^2 + 5
The NOTATION f o g called the ….. and is defined as ……
The compositionof the function f with g and is defined as f(g(x))
What to do when finding a fuction domain such as 7/x^2 - 25?
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)
Find the domain of the function 1/square root of x-1
(1, infinity sign) and NOT [1, infinity sign) We use the [ Only if it was not in the denominator
Find the domain of the function square root 25 - 5x
(- infinity, 5]
Always when the x (in this case 5x) is negative we change the sign > to <
Find the domain of the function square root x -11 + square root x + 1
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)
Find the domain of the function square root x - 2 / x - 6
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)
How would you answer a question with (fg)(x) and a question with f o g
(fg)(x) means f(x) multiply by g(x) while f o g means f(g(x))
interval notation means
The form (infinity, x) or (x,y]
An inverse function means that
f = x and g = x
Find an equation for f^-1(x), the inverse function.
f(x) = x + 7
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
How to determine whether the function has an inverse function or not.
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
How to find if the fuction is increasing, decreasing, or constant
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)
If the arror of the graph points up put the line looks like this \|
Meanse that its decreasing
How to find the relative maximum for x in a graph
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
How to determine whether the graph of the equation is symmetric with respect to the y-axis, the x-axis, the origin
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
An even function will propely look like: h(x) = 4x^2 - x^10
It will stay the same so h(x) = 4x^2 - x^10
Y-AXIS
An odd function will propely look like: f(x) = x^3 + 4x
Both will be negative so f(x) = - x^3 - 4x
ORGIN
A neither function will propely look like: f(x) = x^4 - 2x
One of them will be positive and the other will be negative so f(x) = - x^4 - 2x
NEITHER
You round down to the nearest year even if the answer
even if it was 2024.6 which is a number that is bigger than 5
In word questions, usually the equation f(x) will be
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)
In a word equation that have f(x) and g(x) means
The functions will be diffrent
In a word equation, 90% means
0.9
In a word equation, 90% means
0.9
How to find the center and radius of the circle? (x-2)^2 + (y+5)^2 = 49
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
How to write the equation of the circle in standard form? x^2 + y^2 - 6x + 8y - 11 = 0
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)
How to find the vertex and the coordinates?
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)
How to determine if a function has a minimum or maximum value?
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
RANGE ISSSS
All the points of y in the graph where the domain is all the points of x in the graph.
Varies directly
y=kx and varies jointely is the same but with two variables e.q y=kab
Varies inversely
y=k/x
A=p(1+r/n)^ni
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
