Unit 3 Study Guide: Functions, Relations & Conics
I.
Domain and Range
1. Domain is all the __-values and listed from ________ to _________.
Range is all the __-values and listed from ________ to _________.
2. List the domain and range for each of the following graphs.
3.
Unit 3 Study Guide: Functions, Relations & Conics
II.
Equations of Conics
1. Fill in the following chart.
Four Types of Conics
Equation
Special Characteristics
Meaning of Variables
(not including x and y)
C__________
E__________
H___________
Vertex Form only
P___________
2. Tell what type of conic the following equations would make.
3.
4.
(𝑥−3)2
−
(𝑦−2)
9
=1
A. x² + y² = 25
C.
B. 9x² + 16y² = 144
D. 4𝑥 2 − 12𝑦 2 = 48
4
Unit 3 Study Guide: Functions, Relations & Conics
III.
Circles
1. A. What is the equation of the circle with center at (5, -3) and radius of 4?
Think About It: Is the point (5, 1) on the circle? Is (2, 3) on the circle? How can you check this?
2.
3.
4.
A circle with the equation 𝑥 2 + 𝑦 2 = 81 has been shifted 2 units left and 3 units up.
What is the new equation of the circle?
Unit 3 Study Guide: Functions, Relations & Conics
IV.
Ellipses
1. Write the equation for the following ellipse.
2. Graph the following:
A.
3.
(𝑥−2)2
4
+
(𝑦+4)2
9
=1
B. 16𝑥 2 + 25𝑦 2 = 400
Unit 3 Study Guide: Functions, Relations & Conics
V.
Hyperbolas
1. What is the difference in the graph of the hyperbola if the x² is in front compared to the
y² being in front of the equation?
2. Graph the following hyperbolas.
A.
𝑥2
25
−
𝑦2
4
=1
B. 9(𝑦 − 2)2 − 4(𝑥 + 1)2 = 36
3. Write the equation of the hyperbola.
4.
Unit 3 Study Guide: Functions, Relations & Conics
VI.
Parabolas
1. Using the graphing calculator, graph and label the x-intercepts, y-intercept, vertex,
maximum or minimum of 𝑦 = −3𝑥 2 + 4𝑥 + 2. Be sure to specify the points.
2. Graph 𝑦 = −2(𝑥 + 3)2 + 4.
3. A parabola, y = x², has a center at (0, 0) and a = 1. If the equation is changed to 𝑦 =
−(𝑥 + 3)2 − 2, how will that change the graph of the parabola?
Unit 3 Study Guide: Functions, Relations & Conics
VII.
Intercepts
1. Another name for x-intercepts are ___________ or ____________.
2. You can find x-intercepts by substituting ____ in for the y-value. You can find yintercepts by substituting _____ in for the x-value.
3. Find the intercepts for the following conics.
A. 𝑥 2 − 𝑦 2 = 225
B. 𝑦 = 4𝑥 2 − 𝑥 − 5