Download line - Brenda Womack

Strategies for Success
GOOD LUCK!!
Strategy 1

Can I plug it in?
Strategy 2

Can I graph it?
Strategy 3

Can I make a table of
values?
Strategy 4

Can I draw a picture?
Function



Each “x” is paired with exactly one y
x cannot repeat
The vertical line test can be used to
determine whether a relation is a function
How it’s tested
Independent Variable



The input or “x” variable
Will be graphed on the “x” axis.
Will be on the right side of the equation.
Dependent Variable
The output or “y” variable
 Will be graphed on the “y” axis
 Will be on the left side of the
equation.

C=40+25h
Dependent
Independent
Variable
Variable
C
O
S
T
# of hours
How it’s Tested
Domain

Set of allowable “x” values
Range

Set of allowable “y” values
How it’s Tested
What is the domain of this function?
a) -3 < y < 3
b) -3 < y < 3
c) -3 < x < 3
d) -3 < x < 3
Correlation


On overall pattern in the data of a
scatterplot
The three types of correlation tested on
the TAKS are positive, negative, and no
correlation.
How it’s tested
Mapping

A pair of ovals which show how x and y are
paired.
x-intercept
Point where graph touches x-axis
Point will be written (a, 0)
To find the x-intercept, plug in 0 for y and
solve
y-intercept



Point where graph touches the y-axis
Point will be written (0, b)
To find the y-intercept, plug in 0 for x and
solve.
How it’s tested
What is the x-intercept
the function f(x) = 3x + 6
a) (6, 0)
b) (0. 6)
c) (0. -2)
d) (-2, 0)
Slope



Indicates the steepness of a line
Rise/Run
Rate of Change
y 2  y1
m
x2  x1
How it’s tested
What is the rate of
change for the graph
below?
What is the slope of the
equation 2x – 5y = 10?
a) 2/5
b) 5/2
c) -2/5
d) -5/2
Parent Function


The simplest form of a function family
There will be two parent functions tested
on TAKS: Linear and Quadratic
How it’s tested
Parameter Changes in Linear
Functions



In the linear function y = mx + b, m and b are
called parameters.
When the slope or “m” is changed, the only
thing effected is the steepness of a line.
When the y-intercept or “b” is changed, the
line moves up or down the y-axis.
How it’s tested





The line y = ¾ x is drawn on a coordinate grid. A
second line is drawn with a slope of 1. Which statement
best describes the relationship between these two
graphs?
A) The second line is steeper than the first line
B) The graphs are perpendicular lines
C) The second line is less steep than the first line
D) The graphs are parallel lines
Parameter Changes in Quadratic
Functions



In a quadratic function of the form y = ax2 + c, “a” and
“c” are called parameters.
The value of “a” affects the width of the parabola
Changing the value of “c” will cause a translation up or
down.
How it’s tested
System of Equations



Two or more linear equations that use two
or more variables.
The solution to a system is a pair of
numbers that makes both equations true.
On the TAKS, anytime you see two
equations in the same problem, solve
them both for y and then graph on your
calculator.
TAKS Examples: Systems
TAKS Examples: Systems
Roots, Solutions, Zeros

The x-intercepts of a function
Complementary Angles

Two angles whose sum is 90 degrees
a
b
Supplementary Angles

Two angles whose sum is 180 degrees
a
b
Dilation




A proportional enlargement or reduction of a
figure.
The size of the enlargement or reduction is
called the scale factor of the dilation
If the dilated image is larger than the original,
then the scale factor > 1. This is called an
enlargement.
If the dilated image is smaller than the original
figure, then the scale factor < 1. This is called a
reduction.
Example Of Dilation
Reflections



A mirror image of a figure across a line.
The line is called the line of reflection.
A figure and its reflected image are always
congruent.
Translation



A movement of a figure along a line
Can be described by stating how many
units to the left or right the figure is
moved and how many units up or down it
is moved.
A figure and its translated image are
always congruent
Net

A 2-dimensional representation of a 3dimensional object.
How it’s tested
Parallel Lines

Two lines which have the same slope
Perpendicular Lines


Lines which intersect
at 90 degree angles.
Two lines whose
slopes are negative
reciprocals of each
other.
Similar Figures



Same shape
Corresponding Angles of similar figures
are congruent
The lengths of corresponding sides are
proportional
How it’s tested
Right Triangles

Use the Pythagorean
theorem when you
know 2 sides and
need a 3rd
Right Triangles

Use the properties of
special right triangles
when you only know
________ side.
Distance Formula

Use whenever you
need to find the
length of a line
segment.
Midpoint Formula

Use whenever you need to find the midpoint
or “half-way” point of a line segment.
Arc of a Circle




Part of circle determined by
any two points on the
circle.
The length of an arc is
proportional to the
circumference of the circle.
The length of an arc can be
found by setting up and
solving a proportion.
There are 360 degrees in a
circle.
Sector of a Circle



Part of a circle bounded
by two radii and an arc.
Shaped like a piece of
pie.
The area of a sector of a
circle is proportional to
the area of the circle.
Resetting the Memory
Friendly Viewing Window


When tracing functions on the graphing
calculator, it is helpful to have a “friendly”
viewing window.
To obtain a “friendly” window, you must
use multiples of 9.4 in the x min and x
max.
Zoom 6

When you want the “standard” 10 by 10
window, on your graphing calculator,
press zoom 6.
Zoom 0


Zoom Fit Window
Use this window, to fit the function you
have in y = .
Table Setup



Press 2nd Window to set up your table
At TblMin tell the calculator where you
want the table to start.
At
Tbl, tell the calculator what to go up
by.
Solve Algebraically, Confirm
Graphically
Solve Graphically, Confirm
algebraically