Graphing Calculator For Rational Functions (20-1)

Question 1

How do you graph a rational function on a TI-84/T184?

Answer 1

Press Y=, type your function (e.g., Y1 = (X^2-1)/(X-2)), then GRAPH. Adjust the window to see important features like intercepts and asymptotes.

Question 2

How do you find vertical asymptotes using a graphing calculator?

Answer 2

Graph the function and look for values of X where the function approaches infinity (the curve “shoots up/down”). These X-values correspond to where the denominator = 0. Use TABLE or ZOOM→Trace for precision.

Question 3

How do you find horizontal or oblique asymptotes?

Answer 3

Look at the graph as X becomes very large (+/-). Horizontal asymptotes correspond to the value Y approaches; oblique asymptotes appear as a slanted line. You can also compare degrees of numerator and denominator:
- deg(P) < deg(Q) → Y=0
- deg(P) = deg(Q) → Y = leading coefficients ratio
- deg(P) = deg(Q)+1 → oblique asymptote (use long division)

Question 4

How do you find X-intercepts of a rational function?

Answer 4

Enter the function, GRAPH, then 2nd → TRACE → zero. Move the cursor near the intercept and press ENTER.

Question 5

How do you find Y-intercepts?

Answer 5

Enter X=0 into the function using 2nd → TRACE → value, or check the table at X=0.

Question 6

How can you solve equations like (X^2-1)/(X-2) = 3 using a graphing calculator?

Answer 6

Enter two functions:
- Y1 = (X^2-1)/(X-2)
- Y2 = 3
Press GRAPH, then 2nd → TRACE → intersect. The X-values at intersections are the solutions.

Question 7

How do you check solutions for rational function equations?

Answer 7

Plug the solution back into the original function using 2nd → TRACE → value. Make sure the denominator ≠ 0 for validity.

Question 8

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

Answer 8

Modify the function in Y=:
- Vertical shift: Y1 = ((X^2-1)/(X-2)) + 2
- Horizontal shift: Y1 = ((X-1)^2-1)/(X-2)
- Vertical stretch: Y1 = 3*((X^2-1)/(X-2))
Then GRAPH to observe changes.

Question 9

How do you use the table function for rational functions?

Answer 9

Press 2nd → TABLE. Adjust TblStart and ΔTbl in TBLSET to quickly see f(x) values without manually evaluating each X.

Question 10

Practice card: Graph Y = (X^2-4)/(X-2) and identify vertical asymptotes.

Answer 10

Graph function, notice curve shoots up at X=2. Vertical asymptote: X=2.

Question 11

Practice card: Graph Y = (X-1)/(X^2+X-6) and find horizontal asymptote.

Answer 11

Graph function; as X→∞, Y→0. Horizontal asymptote: Y=0.

Question 12

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

Answer 12

Enter Y1=(X^2-1)/(X-2), Y2=2, GRAPH, 2nd → TRACE → intersect. Solution: X ≈ 3.561 (calculator value).

Question 13

Practice card: Graph Y = 2/((X+1)(X-3)) and describe transformations.

Answer 13

Vertical stretch factor 2, horizontal shifts at X=-1 and X=3. Graph shows asymptotes at X=-1 and X=3, horizontal asymptote at Y=0.