Sharp EL9900 manual Slope and Intercept of Absolute Value Functions, If x ≥

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EL-9900 Graphing Calculator

Slope and Intercept of Absolute Value Functions

The absolute value of a real number x is defined by the following:

x =

x if x

0

 

-xif x

0

If n is a positive number, there are two solutions to the equation f (x) = n because there are exactly two numbers with the absolute value equal to n: n and -n.The existence of two distinct solutions is clear when the equation is solved graphically.

An absolute value function can be presented as y = ax - h + k. The graph moves as the changes of slope a, x-intercept h, and y-intercept k.

Example

Consider various absolute value functions and check the relation between the graphs and the values of coefficients.

1. Graph y = x

2. Graph y = x -1 and y = x-1 using Rapid Graph feature.

Before There may be differences in the results of calculations and graph plotting depending on the setting. Starting Return all settings to the default value and delete all data.

Set the zoom to the decimal window:

ZOOM

 

A

(

ENTER

 

2nd F

 

 

)

7

Step & Key Operation

Display

Notes

1-1Enter the function y =x for Y1.

Y= MATH B 1 X//T/n

1-2View the graph.

GRAPH

Notice that the domain of f(x)

=x is the set of all real num- bers and the range is the set of non-negative real numbers. Notice also that the slope of the

graph is 1 in the range of X > 0 and -1 in the range of X 0.

2-1

2-2

10-1

Enter the standard form of an abso- lute value function for Y2 using the Rapid Graph feature.

Y=

 

 

 

ALPHA

 

A

 

MATH

 

B

1

X//T/nALPHA H + ALPHA K

Substitute the coefficients to graph y = x - 1.

2nd F SUB 1 ENTER 1 ENTER

0 ENTER

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Contents EL-9900 Contents Read this first Always read Before StartingUsing this Handbook IntroductionFractions and Decimals ExamplePie Charts and Proportions BeforeSlope and Intercept of Linear Equations 1Enter the equation y = x for Y2 Parallel and Perpendicular Lines 2View the graphs Slope and Intercept of Quadratic Equations 1Change the equation in Y2 to y = x 2+2 1Access the Solver feature This screen will appear a few 4Enter the values L=15,000, I=0.09, N=48 Access the Solver feature 10π 200 15 π1Access the Solver feature 5Solve for the height and enter a starting point Graphing Polynomials and Tracing to Find the Roots 1Move the tracer near the left-hand root Graphing Polynomials and Jumping to Find the Roots = x 4 + x 3 5x 2 3x +Find the next root Solving a System of Equations by Graphing or Tool Feature 1Access the Tool menu. Select the number of variables Entering and Multiplying Matrices 1Multiply the matrices a and B together at the home screen Solving a System of Linear Equations Using Matrices 2Calculate B-1C Solving Inequalities EL-9900 Graphing Calculator Solving Double Inequalities 2x 5 ≥= 2x 5 = 2x 5 and y = 7 intersect at 6,7 + y ≤ 2x + y ≥+ y ≤ + 2y ≤ 1 x 2 + y ≥ + 2y ≤ 1 y ≤ +y ≥ 4 y ≥ 4 xContinuing key operations omitted Slope and Intercept of Absolute Value Functions If x ≥3View the graph Solving Absolute Value Equations Solve an absolute value equation 5 4x =Solving Absolute Value Inequalities = 10, y =2nd F Calc 2 x = = 9.999999999 Note Evaluating Absolute Value Functions +3 1+3Math Graphing Rational Functions + 1x Solving Rational Function Inequalities Graphing Parabolas = y 2 + 2 = y = +√ x +Change to parametric mode Graphing Circles Graph x 2 2x + y 2 + 4y =2x + y 2 + 4y = 2x + y+22 =For Y1 = Y1 2 for Y2, and y = -Y1 -2 for Graphing Ellipses View the graph Graphing Hyperbolas Zoom out the screen Key pad for the Sharp EL-9900 Calculator Key pad for the Sharp EL-9900 Calculator Sharp Graphing Calculator Step Sharp Corporation OSAKA, Japan