Polynomial Functions & Their Graphs — Drills
Polynomial Functions & Their Graphs has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Factor — A number that divides evenly into another.
- y-intercept — The output when x = 0 — where the line crosses the vertical axis.
- Polynomial — A sum of terms, each a number times a whole-number power of the variable.
- Roots — The x values where y = 0.
- Leading coefficient — The number in front of the highest power. Its sign decides which way the right end goes.
- Multiplicity — How many times a root repeats. It decides whether the graph crosses or just touches.
- Turning point — Where the graph changes from rising to falling or back. At most n - 1 of them.
Degree
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is the degree of 6x5 - 5x3 + 7?
Worked answer
5
The powers present are 5, 3 and 0
The highest is 5
Problem 2
What is the degree of 1x2 - 4x5 + 7?
Worked answer
5
The powers present are 2, 5 and 0
The highest is 5
Turns
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is the greatest number of turning points a degree 6 polynomial can have?
Worked answer
5
At most n-1 = 5
Problem 2
What is the greatest number of turning points a degree 7 polynomial can have?
Worked answer
6
At most n-1 = 6
Mindegree
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A graph has 2 turning points. What is the smallest degree it could be?
Worked answer
3
n-1 ≥ 2
So n ≥ 3
Problem 2
A graph has 4 turning points. What is the smallest degree it could be?
Worked answer
5
n-1 ≥ 4
So n ≥ 5
Roots
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the roots of y=(x-4)(x+5), smallest first, separated by a comma.
Worked answer
-5,4
x-4=0 gives 4
x+5=0 gives -5
Problem 2
Give the roots of y=(x-5)(x+4), smallest first, separated by a comma.
Worked answer
-4,5
x-5=0 gives 5
x+4=0 gives -4
Yint
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the y-intercept of y=(x-5)(x+4)(x-2).
Worked answer
40
(-5)(4)(-2)
=40
Problem 2
Find the y-intercept of y=(x-1)(x+3)(x-4).
Worked answer
12
(-1)(3)(-4)
=12
Degreefac
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the degree of y=(x-1)1(x+3)3.
Worked answer
4
1+3=4
Problem 2
Give the degree of y=(x-1)2(x+3)2.
Worked answer
4
2+2=4