24
INTRODUCTION
(a) y = -2 - x (b) y = x3- x
(c) y = x - (d) j -
x(e) y = x3 (f) y 2 sin x - 2
4. Let f be the function given by the equation = x2 - x + 2. Evalate:
(a) f(0) (b) f) (c) f(-2) (d) f(b)
5. Let g e the fnmtion that is defned by the equation x = 16t + 301. Evalute:
(a ) 0 (b) g(1) (c) g(a) (d) g(x)
6. LetF be the nction that is defined by the equation y= 1 (1 + sin x) where xis in
radians Evaluate:
(a) F( 2) () (c) (0) (d) F(1)
7. State whih of the functions of Problem1 are one-to-one mappings and for eah
such function give a table for the inverse function.
8. State which of the following functions are one-to-one and, for eah give a frmula
for the inverse function:
(a) y = 2x b) = 5x- 7 (c) = x
(d) y (e) y f) x -1
9. Absolute-value function. To eah x, we ssign the absolute value of x, xl, thereb
defning a funetion: = 1xl.
(a) What are the domai and range?
(b) Evaluate -3j, ', -7.
(c) Graph the unction.
10. For each of the following geometri quantities give an appropriae formula, nd
interpret the formula as a fiction by giving the domain and rang in each case:
(a) The area of a square of iven side.
b) The volume of a sphere of given radius.
(c) The surface area of a sphere of gven radis.
(d) The altitude of an equilateral triangle of iven side.
(e) The hypotenuse of an isosceles rigt triangle of given legs
11. Find all (real) zeros of each of the polynomials d give the multiplicity of each zero:
(a) x-2 (b) x2 -2 (c) 2 -2x+ 1
(d) x2 - 3x - 4 (e) (x - 1)(x +2)(x + 1)2 (f) +
12. Interpret as a function of several variables and state which is a polynomnial:
(a) The area of a rectangle of given sides.
b) The hypotenuse of a right triangle of given egs.
(c) Te altitude on side c of an isosceles trianle of sides a a, c.
(d) The speed ter t seconds of a particle strting from rest and moving on a straigt
line with acceleration a (in feet per second per second)
(e) The product of the roots plus twice the sumn of the roots of the qadrati eqnation ax + bx + c = 0.
0-13 GRAPH OF A SECOND DEGREE POLYNOMIAL
We consider a function given by
y = ax2 + bx + c, a 0- 0
(0-130)
