Study all homework and exercises

**1**.**1
a**.
Find the intercepts of and graph the
line 5

**b**. Find the distance,
between two given points. Find the midpoint
of two given points. e.g. find the
distance and midpoint of the points (4.6,-3)
and (6,2.5).

c. Equation of circle in standard form is:
(x-h)^{2} + (y-k)^{2}=r^{2} where (h ,k) is the center and
*r *is the radius. For examples, find the equation
of the circle if (i) r=,
center (-1,4); (ii) center =(3,-6)
and passing through the point
(0, 4). Find the center and radius of the circle for (x-3)^{2}
+ (y+5)^{2} = 9.

**1**.**2
a**. Determine a relation expression whether it is
a function, and identify the domain and range.

For examples, {(4,-14),(5,8),(0,19),(6,8)} and

Study the questions 15-20, 35-39, and 55-61.

**b**. Find the function values. e.g. f (x)
= 6x^{2} - 9x, find f(2),f(10),f(-x),f(1-h)
and f (x+h).

**c**. Find the domain for a give function. e.g.
f (x)
= x^{2} + 10x + 15,,

**1**.**3
a**. Slope =
, e.g. find the slope of the straight line passing through
(8,-2)and (-1,5); Graph the linear equation and determine its slope (a) 4

**b**. Study word problems Questions 41-44 and 49.

**i**. The average weight of a baby born in 1900 was 6. 25
pounds. In 2000, the average weight of a newborn was 6. 625 pounds. we will assume for our
purposes that the relationship is linear. Find an equation that relates the year
to average weight of a newborn. Using that equation, predict the average weight of a
newborn in 2035.

**1**.**4
a**. Write a
slope-intercept equation for a line with the given conditions e.g. determine the equation of a straight if (i)

**b**. Write equations of the horizontal and vertical lines
which passes through (9,-5).

**c**. Transform the equation of the straight line from general
form to the slope intercept form.

e.g.: Find the slope and *y*-intercept of 7*x *+ 4*y
=
*10.

**d**. Determine the equation of the straight line which is
parallel or perpendicular the given line

e.g. parallel/ perpendicular to the line 2*x *- 5*y = *
10 and containing the point (9,3), and questions 75 to 80 on pp. 116-117.

**1**.**5
a**. In Figure 1 above,
determine the intervals on which the function is (a) increasing, (b) decreasing, (c) constant, (d) relative maximum or minimum.

**b**. Study the word problems Questions 31-34 on pp. 129-130.

c. Know how to find the function value of a piecewise function.
For example, compute the function value for piecewise function e.g.

,
find f(-1) and f(6).

**1**.**6**

**a**. Find (f + g)(x),(f - g)(x),(f•g)(x),
and (f/g)(x) ; determine their domains. e.g.

f(x) = 5x - 8 and

**b**. Know how to graph and find the domain the
function of *f *+
*g *if the graphs of *
f*(x) and *
g*(x)
are given.

**c**. Find
if f (x) = 8x^{2} + 15x

**d**. Find
and
and their domain if (a) f
(x)=9*x
*+ 4 and
,
(b) f
(x)=
2x + 5 and.

**e**. Find f(x) and g(x)
such that
when
.

**1**.**7
a**. Given a graph, should know whether it is
symmetric with respect to the

**b**. Vertical shift: *y *f(x)
+ *k*;
Horizontal shift: y = f(x- h);
Vertical stretch/compression:
y = af(x);
Horizontal stretch/compression y
= f(ax);
Reflection to the *x*-axis
*y
*= -f(x) and reflection to the *y*-axis
y =f(-x).
For examples, write the function and sketch the corresponding graph of
* *, but is (a) shifted left by 3 units; (b)
shifted down by 5 units; (c) vertically sketched by factor of 2 and
shifted up by 3 units; (d) reflection about the
*x*-axis. Also, suppose that you
are given the graph of f(x) = x^{2},
graph the functions g(x) = 4(x-1)^{2} - 2 and
.

**2**.**3
**Methods to solve quadratic
equations include **FACTORING, COMPLETING THE SQUARE, QUADRATIC FORMULA**.
For examples, solve x^{2} - 6x - 16; 2x^{3} - x^{2} - 6x = 0; 3t^{2} + 5t - 3 = 0 by using
any method mentioned above. Use completing square to solve 2x^{2} + x - 1 = 0

**2**.**4
a**. Find the vertex, axis of symmetry, maximum or
minimum value of the function if y = -(x - 6)

**b**. Quadratic function is defined as f(x) = ax^{2} +
bx + c. The graph of f(x) is opened upward if a>0 and downward if a<0.

**c**. Vertex of f(x) is: ,
axis of symmetry is . For example, determine
the functions whether they are open up or down, find the vertex, whether there
is maximum or minimum value, range, intervals of increasing and decreasing of
f(x) = -2x^{2} + 3x + 5 and g(x) = 4x^{2} - 2x + 1. Sketch the graph of the function.

**d**. Know how to solve word problems. Study the
questions 37-45 on pp. 227 - 228.