Graphing Calculator Absolute Value And Reciprocal (20-1)

Question 1

How do you enter an absolute value function on a TI-84/T184 graphing calculator?

Answer 1

Press Y= → type abs(X) using 2nd → VARS → NUM → 1:abs( → complete your function, e.g., Y1 = abs(X-3)+2 → GRAPH to see the V-shaped graph.

Question 2

How do you find the vertex of an absolute value function using the calculator?

Answer 2

Enter the function → GRAPH → 2nd → TRACE → 3: minimum (or maximum if inverted). The calculator shows the X and Y coordinates of the vertex.

Question 3

How do you graph a reciprocal function on a graphing calculator?

Answer 3

Enter Y1 = 1/X → GRAPH. This shows the hyperbola with vertical and horizontal asymptotes at X=0 and Y=0.

Question 4

How do you find and check vertical and horizontal asymptotes using the calculator?

Answer 4

• Vertical: Look where function is undefined (X=0 for 1/X)
• Horizontal: Use TABLE (2nd → GRAPH) with large positive/negative X values to see Y approaches 0.

Question 5

How do you transform absolute value or reciprocal functions on the calculator?

Answer 5

• Shifts: Y1 = abs(X-2)+3 → right 2, up 3
• Reflections: Y1 = -abs(X) → reflect over X-axis, Y1 = -1/X → reflect reciprocal over X-axis
• Stretches/compressions: Y1 = 2abs(X) → vertical stretch, Y1 = 0.51/X → vertical compression

Question 6

How do you find intercepts of absolute value and reciprocal functions using the calculator?

Answer 6

• Absolute value: GRAPH → 2nd → TRACE → zero → find X-intercepts. Y-intercept: X=0 in TABLE.
• Reciprocal: GRAPH → 2nd → TRACE → zero (note: reciprocal has no X-intercept), Y-intercept: X=0 is undefined.

Question 7

How do you solve equations involving absolute value or reciprocal functions using the calculator?

Answer 7

• Absolute value example: abs(X-3)=2 → Enter Y1 = abs(X-3), Y2 = 2 → GRAPH → 2nd → TRACE → intersect → X ≈ 1, 5
• Reciprocal example: 1/X = 4 → Enter Y1=1/X, Y2=4 → GRAPH → intersect → X=0.25

Question 8

Practice card: Graph Y = abs(X+2)-3. Find vertex and X-intercepts.

Answer 8

Vertex: (-2,-3). X-intercepts: X ≈ -5 and X ≈ 1. Use GRAPH → 2nd → TRACE → minimum and zeros.

Question 9

Practice card: Graph Y = -1/(X-1)+2. Identify asymptotes.

Answer 9

Vertical asymptote: X=1. Horizontal asymptote: Y=2. Use TABLE and GRAPH to confirm behavior near asymptotes.

Question 10

Fun tip: How to check vertex or asymptotes?

Answer 10

Once you think you have your vertex or asymptotes, check using the TABLE feature or by evaluating the function at specific X values to see if your graph matches expectations.