Calculator Jeopardy

What's Happening

100

Graph y = x³ - 6x² + 9x

How many turning points does the graph have?

2

200

Graph y = x⁴ - 4x²

How many x-intercepts does the graph have?

3

300

Graph y= ln(x) - x + 2

How many real solutions (zeros) does the function have?

1

400

Graph y = xe^-x

On what interval is the function increasing?

Increasing from negative infinite to 1

500

Graph y=sin(x)+x/2

How many solutions does
sin⁡(x)+x/2 =2 have on [0,6]?

1

Intersections

100

Find intersection:
y=x², y=4

x = -2, 2

200

Find intersection:
y=x², y=x+2

x = -1, 2

300

Find intersection:
y=e^x, y=3

x = 1.10

400

Find intersection:
y=ln⁡(x), y=x−2

x = 1.84

500

Find all intersections:
y=sin⁡(x), y=0.5x on [0,4]

x = 0, 1.9

Build the Model

100

Solve by graphing. 

x² = 9

x = -3, 3

200

Solve by graphing. 

2x² = x + 3

x = -1, 1.5

300

Solve by graphing. 

sin⁡(x) = 0.3 between [0, 2pi]

x = 0.305, 2.837

400

Solve by graphing. 

e^x=2x

x = 1.26

500

Solve by graphing. 

x³ − 3x = 1

• x≈−1.53
• x≈0.35
• x≈1.18

Max/Min

100

Find max of: 

y = -x² + 4 

4

200

Find min of:

y = x² - 6x +5

-4

300

Find max of:

y = sin(x) + cos(x)

1.414

400

Find max of:

y = xe^-x

0.368

500

Find the x value where: 

y = x³ - 3x has a local minimum

x = 1

Calculator Strategy

100

You graph a function but see nothing. What’s your first move?

Adjust window / use ZStandard

200

How can you find a zero more precisely after estimating with table?

Use CALC → zero

300

When should you use table instead of graph?

When looking for patterns or approximate values

400

You only see one intersection but expect two. What likely happened?

Window is too small

500

DAILY DOUBLE

Consider the equations:
y = sin⁡(x) and y = 0.2x²

1. Graph both functions on [0,4]
2. Find all points of intersection on this interval.
3. Determine on which interval(s) sin⁡(x) > 0.2x²

• Intersections:
  • x=0
  • x≈1.63
• Comparison:
  • sin⁡(x)>0.2x² on (0, 1.63)
  • After that, 0.2x² dominates