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IM1.5.7 Calculator Skills

Author:Lind, Jon

See an equation as two functions

Let's look at our opening problem again: Think about this problem as two functions, one for the left side and one for the right side: and . Follow the directions for solving this equation on your calculator, and enter the solutions below.

Keystrokes

Keystrokes
From a blank screen, follow the above keystrokes to graph your equations.

Graphed equations

Graphed equations
This is what your screen should look like now.

Solving with a table

Solving with a table
Press the keys above to see a table of values for both functions. Where do the functions have the same value?

Solving with a graph

Solving with a graph
Press the keys above, then use the arrow keys to move the cursor close to an intersection point, and press enter three times.

Try it on your own

Equation: 1. Write the two functions you will graph on your calculator. 2. Write the intersection points of the two functions. 3. The original equation is true when x= _____ or _____.

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4. Find the solutions to the equation

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Image

5. The graphs of f, a function that involves taking an absolute value, and g a linear function, are shown above. Both functions are defined over all real values for x. Tami concluded that the equation f(x)=g(x) has no solution. Do you agree or disagree? Explain your reasoning.

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