Diagnostic Test Calculus. Calculus Early Trascendentals 8th edition
Diagnostic Test: Functions
The graph of a function f is given at the left.
(a) State the value of f s21d.
(b) Estimate the value of f s2d.
(c) For what values of x is f sxd − 2?
(d) Estimate the values of x such that f sxd − 0.
(e) State the domain and range of f.
If f sxd − x3, evaluate the difference quotient
f s2 1 hd 2 f s2d
h
and simplify your answer.
3. Find the domain of the function.
(a) f sxd −
2x 1 1
x2 1 x 2 2
(b) tsxd −
s3 x
x2 1 1
(c) hsxd − s4 2 x 1 sx2 2 1
4. How are graphs of the functions obtained from the graph of f ?
(a) y − 2f sxd (b) y − 2 f sxd 2 1 (c) y − f sx 2 3d 1 2
5. Without using a calculator, make a rough sketch of the graph.
(a) y − x3 (b) y − sx 1 1d3 (c) y − sx 2 2d3 1 3
(d) y − 4 2 x2 (e) y − sx (f) y − 2sx
(g) y − 22x (h) y − 1 1 x21
6. Let f sxd − H1 2 x2

(a) Evaluate f s22d and f s1d. (b) Sketch the graph of f.
7. If f sxd − x2 1 2x 2 1 and tsxd − 2x 2 3, ind each of the following functions.
(a) f 8 t (b) t 8 f (c) t 8 t 8 t