MATH 0310 Graphing Calculator Supplement

Transcription

1 All instructions reference the TI83/84 family of calculators. All graphs shown use the viewing window x: [-10, 10], y: [-10, 10]. Solving an Equation MATH 0310 Graphing Calculator Supplement The equation x+ = x can be solved using the graphing calculator in the following ways: Using Intersect 4 1. Press and type the left side of the equation into Y1.. Type the right side of the equation into Y. 3. Press. 4. Press to access the CALC menu. 5. Choose option 5:intersect. 6. When asked First curve? press. When asked Second curve? press. When asked Guess?, move the cursor to the desired point of intersection and press. 7. The displayed ordered pair is the point of intersection for the left and right sides of the equation. The x-value is the solution of the equation. Repeat if necessary. The calculator will only find the point of intersection if it is visible on the viewing window. The window may need to be adjusted before completing step 4. Using Root/Zero 1. Solve the equation so zero is on one side of the equal sign. x+ x+ 4= 0. Press and type the left side of the equation into Y1. 3. Press to access the CALC menu. 4. Choose option :zero. 5. Using the left arrow key, move the cursor to a location to the left of the x-intercept and press. 6. Using the right arrow key, move the cursor to a location to the right of the x-intercept and press. Pressing nd then the arrow key will jump the cursor larger distances. 7. When asked Guess? press. The displayed x-value is the solution. Rev: Apr. 11, 013 Page 1 Math 0310 Suppl-GraphCalc-Fall 13-v0 (1) 1

2 Checking the Solution(s) to an Equation Using the Store Feature Solving the equation 3x = 5yields the result x = 9. To check this answer using the graphing calculator, complete the following: 1. On the Home Screen, type the value of the solution followed by and then.. Type the left side of the equation using for the variable and press. 3. Type the right side of the equation using for the variable and press. 4. Verify that the left and right sides produced equivalent values. If one side of the equation is only a numerical value, skip step 3 and verify the desired result. Rev: Apr. 11, 013 Page Math 0310 Suppl-GraphCalc-Fall 13-v0 (1)

3 Evaluating a Function for a Given Value of x 3 Suppose we are asked to evaluate the function f( x) = x x. This can be accomplished using the graphing calculator in the following ways: Using the Table 1. Press and enter the right side of the equation into Y1 using for x.. Press to access TABLE. 3. Scroll using the up and down arrow keys to the desired x- value. For f (), x =. 4. The corresponding value of Y1 from the table is the result: f () = 6. Unless the default Table settings are changed, the Table feature will only calculate for integer values of x. Using Value (Graphing) 1. With the function entered into Y1, press.. Press to access the CALC menu. 3. Choose option 1:value. 4. Type in the desired x-value and press. 1 x= (or.5) y =.375 f ( ) = 8 5. Repeat step 4 as needed. The Value feature of the graph, will only calculate for x-values visible within the current viewing window. Using VARS 1. With the function entered into Y1, return to the Home Screen. ( ). Press followed by the right arrow to access the Y-VARS menu. 3. Choose option 1:Function followed by option 1:Y1. 4. Type an open parenthesis, the desired x-value, and a close parenthesis. Then press. 5. The displayed value is the corresponding function value. Rev: Apr. 11, 013 Page 3 Math 0310 Suppl-GraphCalc-Fall 13-v0 (1) 3

4 Calculating n th Roots Different calculator operating systems require information to be typed in different ways. The TI-83 and the Older TI-84 When a radical is inserted, the calculator includes an open parenthesis. To indicate the end of a radical, type a close parenthesis. The Newer TI-84 The newer operating system displays typed data much as it would be written by hand. When a radical is inserted, the radical symbol stretches across the entire radicand. To exit the radical, press the right arrow key. Square Root To calculate the value of 79 :. Type the value of the radicand, close the parenthesis or exit the radicand, and press. Cube Root To calculate the value of :. Choose option 4: 3 (. 3. Type the value of the radicand, close the parenthesis or exit the radicand, and press. Nth Roots To calculate radicals with an index greater than three, such as : 1. First type the value of the index.. Press. 3. Choose option 5: x. 4. Type the value of the radicand and press. Rev: Apr. 11, 013 Page 4 Math 0310 Suppl-GraphCalc-Fall 13-v0 (1) 4

5 Graphing with Radicals To graph the function f( x) = x : - inside the radical. Press to insert the square root function. 3. Type, then close the parenthesis or exit the radicand and press. 4. Press. To graph the function f( x) = x : - outside the radical. Press to insert the square root function. 3. Type then close the parenthesis or exit the radicand. 4. Type and press. 5. Press. Finding the Minimum or Maximum Value of a Quadratic Function To find the minimum or maximum of f( x) = x x+ 3 using the graphing calculator: 1. Press and type the function into Y1.. Press. The Window may need to be adjusted to display the vertex. 3. Press to access the CALC menu. 4. Choose either option 3:minimum or 4:maximum depending on whether the given function opens upward or downward. 5. Using the left arrow key, move the cursor to a location to the left of the min/max and press. Pressing nd then the arrow key will jump the cursor larger distances. 6. Using the right arrow key, move the cursor to a location to the right of the min/max and press. 7. Move the cursor to the min/max as a guess and press. 8. The displayed value is the ordered pair for the vertex of the parabola: ( 1, 4). The minimum or maximum value is the y- coordinate, 4. Rev: Apr. 11, 013 Page 5 Math 0310 Suppl-GraphCalc-Fall 13-v0 (1) 5