Graphs
Algebra
Formulae
Definitions
Functions
100
The graph of an inverse of a function is a reflection across what line?
y = x (to reflect, simply swap x and y coordinates)
100
Describe using the principle of square roots.
When taking the square root of both sides of an equation to solve it, you must take both the positive and negative square root.
100
What is the Pythagorean Equation?
a2 + b2 = c2
100
What is the slope of a line that goes through the points (x1,y1) and (x2,y2)?
m = (y2 - y1)/(x2 - x1)
100
How do you find the y-intercept (if it exists) of a function f?
Calculate f(0).
200
If a function f has a relative max at value c and relative min at value d, with c < d, then what property does f have on the interval (c,d)?
f is decreasing on (c,d).
200
Describe using the principle of zero products.
An equation with factors on one side and zero on the other is split up into multiple equations, one for each factor, each set to zero.
200
What is the midpoint of two points (x1,y1) and (x2,y2)?
((x1 + x2)/2,(y1 + y2)/2)
200
Describe the Vertical Line Test and what it determines.
If a vertical line crosses a graph more than once, then it is not the graph of a function.
200
How do you find the exact zeros of a polynomial p(x)?
Solve for values of x that make p(x) = 0.
300
If a polynomial function p(x) with degree that is odd and leading coefficient that is negative, what does the end behaviour of the graph of p look like?
The end behaviour of the graph of p is similar to the end behaviour of a line with negative slope.
300
What is the standard form for a quadratic equation?
ax2 + bx + c = 0, for real numbers a,b,c, with a not zero.
300
What is the distance between two points (x1,y1) and (x2,y2)?
√[(x2 - x1)2 and (x2 - y1)2]
300
Define what it means for a function f to have a relative maximum at input c.
There exists some interval (a,b) for which f(c) is the largest output on (a,b).
300
How do you find the equations for the vertical asymptotes of the graph of a rational function f(x)=p(x)/q(x)?
Solve for values of x that make q(x) = 0, but not p(x) = 0 (otherwise the function has a hole instead).
400
How do you find whether the graph of a rational function f(x)=p(x)/q(x) has a hole?
The graph of f has a hole when p and q have a common factor which can equal zero at some input value.
400
When solving an equation that is reducible to a quadratic form, and the substitution variable is u, what is the next step after solving for u?
Replace u with its substituted expression and solve the resulting equations.
400
What is the standard form for the equation of a circle with radius r and centre (h,k)?
(x-h)2 + (y-k)2 = r2
400
Describe the floor (greatest integer) function.
For input x, the floor of x is the greatest integer less than or equal to x.
400
What are the set of inputs, and the set of outputs, for a function called, respectively?
domain (inputs) and range (outputs)
500
What can you describe about the graph of a polynomial function p(x) that has a zero k of even multiplicity.
The graph of p is tangent to the x-axis at (k,0).
500
How can you check that you have done polynomial division correctly?
Multiply the result by the denominator and add it to the remainder.
500
What is the quadratic formula?
x = [-b ± √(b2-4ac)]/2a
500
What is the difference quotient for a function f?
[f(x + h) - f(x)]/h
500
For a rational function f(x)=p(x)/q(x), how is the horizontal asymptote determined?
If degree of p is less than the degree of q, the x-axis is the horizontal asymptote. If the degree of p and q are the same, then the leading coefficient a of p and the leading coefficient b of q gives the horizontal asymptote y = a/b.
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