Graphs
The end behavior of an even-degree polynomial with a positive leading coefficient?
Both ends go up
What causes a vertical asymptote?
A denominator equals to zero
What happens to the transformation when you add to the function?
Vertical shift
What are the zeros of
(x-4)(x+1) = 0
x=4 and x=-1
What is an x-intercept?
The point where the graph crosses the x-axis
What does it mean if a graph is concave up?
The rate of change is increasing
What is the difference between a hole and a vertical asymptote?
A hole cancels but a vertical asymptote does not
What happens to the transformation when you subtract from inside the function?
Shifts right
Solve
x^2-9=0
x = 3, x = -3
Define domain
All possible x-values
What does multiplicity tell you about a zero?
Whether the graph crosses or bounces off the x-axis
What is the horizontal asymptote of f(x) = 3x+1/x-2
y = 3
what transformation does f(x) = -|x| have?
reflection across the x-axis
Factor
x^2+5x+6
(x+2)(x+3)
Define range
All possible y-values
A graph touches the x-axis at x =2 and bounces. What is true about the multiplicity?
It has even multiplicity
What’s the vertical asymptote: f(x) = x+1/x^2-9
x = 3 and x = -3
What to the transformation when a function is multiplied by 2 on the outside?
Vertical stretch
solve
x^2-4x-5=0
x =5 and x =-1
What is a turning point?
A point where the graph changes direction from increasing to decreasing or decreasing to increasing
Describe the end behavior of
f(x) = -2x^5
Rises to the left and falls to the right
When does a rational function have no horizontal asymptote?
When the numerator degree is greater than the denominator degree
What are the transformations of
f(x) = -2(x-3)^2+5
shift right 3, up 5, reflection over x-axis, vertical stretch by 2
What is the degree of
3x^5-2x^2+7
5
What is a rational function?
A function written as one polynomial over another