Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x).
Answer
Transforming Functions: g(x) and h(x) as Variations of f(x)
Transforming Functions: g(x) and h(x) as Variations of f(x)
📊 Tabular Data for Functions
Function: f(x)
Function: g(x)
Function: h(x)
🔍 How to Express g(x) and h(x) as Transformations of f(x)
📌 Step 1: Analyzing g(x)
Compare the x-values and outputs of
g(x) and
f(x):
- Notice that
g(x) appears to be a horizontal shift of f(x).
- For example,
g(0) = f(-2), g(1) = f(-1), and so on.
➤ Therefore,
g(x) = f(x – 2)
📌 Step 2: Analyzing h(x)
Compare the outputs of
h(x) and
f(x) at the same x-values:
h(x) = f(x) + 2 for all x.- Example:
f(0) = 0 → h(0) = 2, f(1) = 1 → h(1) = 3, etc.
➤ Therefore,
h(x) = f(x) + 2
🎯 Final Transformations
- g(x) = f(x – 2) ⟶ Horizontal shift right by 2 units
- h(x) = f(x) + 2 ⟶ Vertical shift up by 2 units
