Chapter 1 (1.2 to 1.9) Flashcards
How do you find x and y intercepts?
X-intercept, plug in 0 for y
Y-intercept, plug in 0 for x
How do you find x-axis, y-axis, and origin symmetry?
X-axis, if you plug in -y it will equal y
Y-axis, if you plug in -x it will equal x
Origin, if you plug in -y and -x it will equal y and x
Ex:
X-axis y^2=x
Y-axis y=x^2
Origin y=2x^3
What is the circle formula?
(X - H)^2 + (Y - K)^2 = R^2
Center is (H,K) Radius is R
What is the slope-intercept form of a line?
Y=mx+b
M is slope and b is y-intercept
What is the distance formula?
–––––––––––––––––––––––
/ (X2 - X1)^2 + (Y2 - Y1)^2
What is the intercept form of a line?
X/a + y/b =1
A is x-intercept
B is y-intercept
What is the standard form of a line and how would you find slope?
ax + by = c
Slope is -a/b
What is the point-slope form of a line?
y - y1 = m(x - x1)
(x1, y1) is a point on a line
M is slope
What is the equation of a vertical line and what is its slope?
X = A
Slope is undefined or no slope
What is the equation of a horizontal line and what is its slope?
Y = B
Slope is zero
What is the slope formula?
Rise Y2 - Y1
–––– or –––––––
Run X2 - X1
How would you identify if lines are parallel or perpendicular by their slope?
Parallel lines m=m, slopes are equal
Perpendicular lines m=-1/m, slopes are opposite reciprocals
How would you identity if something is a function?
Every x has only one y
What is domain and range?
Domain is all possible x
Range is all possible y
What is the midpoint formula?
X1 + X2 Y1 + Y2
——— ———
2 , 2
What are the restrictions on domain?
Cannot divide by zero and cannot square root negative numbers
Is the rate of change formula the same as the slope formula?
Yes
How would you identify odd functions?
They have symmetry in the origin
For all x, f(-x) = -f(x)
How would you find absolute minimum or absolute maximum on a graphing calculator?
2nd Clac minimum or maximum
What is the formula for step functions?
Y = [[x]]
It means the greatest integer contained in x
Ex:
[[.5]] is zero
[[-3.5]] is -4
On graphing calculator MATH, NUM, #5 int(
How would you shift an equation up, down, left, or right?
Up F(x) + c Down F(x) - c Left F(x + c) Right F(x - c)
How would you reflect an equation over the x or y axis?
Y-axis is f(-x)
X-axis is -f(x)
How would you identify even functions?
Have symmetry in the y-axis
For all x, f(-x) = f(x)
How do you find an inverse function?
Switch x and y
Solve for y
Change y to f^-1(x)
How do you check an inverse function?
(fog)(x)=(gof)(x)=x
How can you check if a function has an inverse with a graph or a table?
If is passes the horizontal line test
One to one (every x has one y and every y has one x)
How would you do a sum (f+g), difference (f-g), product (fg), quotient (f/g), or composition function (fog)?
Add, subtract, multiply, divide, or insert into x (f(g(x))
What would the integer function of Y=((x)) look like?
Closed on zero, zero open on one, zero
