Graphing Calculator For Exponential And Logarithmic (20-1)

Question 1

How do you graph an exponential function on a TI-84/T184 calculator?

Answer 1

Press Y=, type your function (e.g., Y1 = 2^X), then press GRAPH. Adjust the window if needed (WINDOW key) to see the curve properly.

Question 2

How do you adjust the viewing window for an exponential function?

Answer 2

Use the WINDOW key:
- Xmin/Xmax for horizontal range (e.g., -5 to 5)
- Ymin/Ymax for vertical range (e.g., -1 to 10)
This ensures you can see the important part of the curve.

Question 3

How do you find the value of an exponential function at a specific x-value using the graphing calculator?

Answer 3

After typing the function in Y=, press 2nd → TRACE (CALC) → value. Enter the x-value and the calculator shows f(x).

Question 4

How do you graph a logarithmic function?

Answer 4

In Y=, type your function (e.g., Y1 = log(X) or ln(X)), then GRAPH. Make sure Xmin > 0 because log functions are undefined for x ≤ 0.

Question 5

How do you evaluate a logarithmic function at a specific point on a graphing calculator?

Answer 5

Use 2nd → TRACE → value. Enter the x-value (must be >0), and the calculator displays log(x) or ln(x).

Question 6

How do you solve equations like 2^x = 8 using a graphing calculator?

Answer 6

Enter two functions:
- Y1 = 2^X
- Y2 = 8
Press GRAPH, then 2nd → TRACE → intersect to find where they meet. This gives the solution for x.

Question 7

How do you solve equations like log(X) = 3 using a graphing calculator?

Answer 7

Enter two functions:
- Y1 = log(X)
- Y2 = 3
Press GRAPH, then 2nd → TRACE → intersect. The x-value at the intersection is the solution.

Question 8

How can you check solutions to exponential or logarithmic equations using your calculator?

Answer 8

Plug the solution back into the original equation using the CALC → value feature. Compare left-hand side and right-hand side.

Question 9

How do you explore transformations (shifts, stretches) of exponential and logarithmic functions on a graphing calculator?

Answer 9

Modify the function in Y=:
- Vertical shift: Y1 = 2^X + 3
- Horizontal shift: Y1 = 2^(X-2)
- Vertical stretch: Y1 = 3*2^X
Then GRAPH and observe the changes.

Question 10

How do you use the table function to see multiple values for exponential/log functions quickly?

Answer 10

Press 2nd → TABLE. Adjust TblStart and ΔTbl in the TBLSET menu. This allows you to see f(x) for multiple x-values without entering each individually.

Question 11

How can you estimate the solution to an equation visually before calculating it precisely?

Answer 11

Graph both sides as functions, look at the intersection point, and estimate the x-value. Then use CALC → intersect for exact value.

Question 12

Practice card: Graph Y = 3^X and find Y when X = 2.

Answer 12

Enter Y1 = 3^X, GRAPH, then 2nd → TRACE → value, enter X=2. Result: Y=9.

Question 13

Practice card: Graph Y = ln(X) and find X where Y = 1.

Answer 13

Enter Y1 = ln(X), Y2 = 1, GRAPH, 2nd → TRACE → intersect. X ≈ 2.718.

Question 14

Practice card: Solve 2^(X-1) = 16 using the graphing calculator.

Answer 14

Enter Y1 = 2^(X-1), Y2 = 16, GRAPH, 2nd → TRACE → intersect. X = 5.

Question 15

Practice card: Graph Y = log(X-2) + 3 and describe the transformations.

Answer 15

Horizontal shift right 2, vertical shift up 3. Use GRAPH to visualize.