Parent Function Stuff
The equation for slope-intercept form is
y=mx+b
What is a zero and how do you solve for it?
x-intercept
set y=0, solve by dividing/factoring
The 4 types of conics are
circles, ellipses, parabolas, hyperbolas
The solution of a system of equation is
the point where the two lines intersect
True or False: both f-1(f(x)=x and f(f-1(x)=x must occur for two functions to be inverses
What is a function.
every input has exactly one output, passes the vertical line test
A function changes from +/- or -/+ at
Critical points: zeroes and vertical asymptotes
What's the difference in calculating the foci of an ellipse versus a hyperbola
Hyperbola: c2=a2+b2
Ellipse: c2=a2-b2
You are solving a 3x3 system of equations and end up with 0=0. This equation has how many solutions?
infinitely many
What are the two types of logarithmic equations and how do you solve them?
Type 1: all parts of the equation have logs, both sides are combined into a single log and then the logs can be dropped
Type 2: one part of the equation doesn't have a log, combine all the logs into one on one side and then use the inverse rule to rewrite the equation as an exponential
Where is the function increasing, decreasing, and constant
increasing: (-4,0)
decreasing: (-9,-5)
constant: (0, inf)
Write the equation of the horizontal/slant asymptote.
x4-3x4+2x2-5 /
-3x5+6x3-5x2-4x+12
y=0
Identify the centre, and whether the function opens up and down or left and right
(𝑦+2)2/25-(𝑥−3)2/16=1
centre: (3,-2)
opens up and down
You are solving a 3x3 sytem of equations using cramer's rule and find the following determinants:
Dx=18 Dy=-6 Dz=-12 D=6
find x,y, and z
(3,-1,-2)
fill in the blank for completing the square
2x2-8x+6
2(x__)2__+6
2(x-2)2-8+6
rewrite the equation as an exponential
log61/36=-2
6-2=1/36
List out all the possible zeros
(2x-3)(x+4)(x-1)
+/- 1,2,3,4,6,12,1/2,3/2,
Identify each type of conic
A) (y−4)2/9−(x+1)2/36=1
B) (y−7)2=x+3
C) x2+y2=81
D) (x−3)2/4+y2/16=1
A) hyperbola
B) parabola
C) circle
D) ellipse
Find the determinant of the matrix
1 -3 1
3 2 1
-2 -1 -4
-36
create two equations that make up the piecewise functions plus the cutoffs
x+5 x<-2
-2 x≥-2
The 10 parent functions are
identity/linear, quadratic, square root, cubic, cube root, absolute value, reciprocal, exponential, logarithmic, constant
The critical values for the function
f(x)=(5x-3)(x+6)/(x+4)3
are -6 -4 3/5.
Where is the function ≥0 in interval notation.
[-6,-4)U[3/5,∞)
create the equation for an ellipse with:
Endpoints of major axis: (2, 2) & (8, 2)
Endpoints of minor axis: (5, 3) & (5, 1)
(𝑥−5)2/9 + (𝑦−2)2/1 = 1
State the operation occurring between the two matrices
1 2 -1 | 2 1 2 -1 | 2
0 1 -2 | -4 0 1 -2 | -4
0 -3 3 | 3 0 0 -3 | -9
3R2+R3 -->R3
Is there another topic you wished I had asked a question about
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