Math 140
1.4: The Graph of a Function
Q:
A:
Given the graph of an equation, how do I know if I have a function?
Use the Vertical Line Test (VLT) – see page 42.
 Take the graph
 Draw lots of vertical lines
 0 or 1 touches – function
 2 or more touches – no function
10.
Use the given graph of the function f to answer parts (a) – (n). See page 46.
(a) Find f(0) and f(6).
(b) Find f(2) and f(–2).
(c) Is f(3) positive or negative?
(d) Is f(–1) positive or negative?
(e) For what numbers x is f(x) = 0?
(f) For what numbers x is f(x) < 0?
(g) What is the domain of f ?
(h) What is the range of f ?
(i) What are the x–intercepts?
(j) What is the y–intercept?
(k) How often does the line y = –1 intersect the graph?
(l) How often does the line x = 1 intersect the graph?
(m) For what values of x does f(x) = 3?
(n) For what values of x does f(x) = –2?
Trigonometry
For Problems 12 – 22 on pages 46–47 determine whether the graph is that of a function by using the Vertical
Line Test. If it is, use the graph to find: domain, range, intercepts (if any), and symmetry with respect to the x–
axis, y–axis, or the origin (if any). (For our purposes, regardless of whether or not the graph is that of a
function, we will answer all the questions so that we can practice.)
12.
Function? Y or N.
Domain:
Range:
14.
Yes
or ( –,+) or { x | x is a Real Number }
(0, +) or { y | y > 0 }
No x–intercept; y–intercept: (0, 1)
None
Intercepts:
Symmetry:
16.
18.
20.
22.
Function? Y or N.
Domain:
Range:
Intercepts:
Symmetry:
Function? Y or N.
Domain:
Range:
Intercepts:
Symmetry: