Question

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Explanation:

🆕 New Concept Discovered: Graphing Parent Functions
Recognizing basic shapes of common functions.

Step 1: Analyze the first graph

The first graph shows a horizontal line.

• A horizontal line has a constant \(y\)-value for all values of \(x\).
• This represents a constant function, which has the general equation:

$$ y = c $$

where \(c\) is a constant. Looking at the grid, the line is at approximately \(y = 3\).

Step 2: Analyze the second graph

The second graph shows a curve that starts near a vertical asymptote on the \(y\)-axis (\(x = 0\)), passes through the point \((1, 0)\), and increases slowly as \(x\) increases.

• This shape is characteristic of a logarithmic function.
• The general parent equation is:

$$ y = \log_b(x) $$

Step 3: Analyze the third graph

The third graph shows a V-shaped curve with a sharp corner (vertex) on the \(x\)-axis at approximately \(x = -5\).

• A V-shaped graph represents an absolute value function.
• The general parent equation is:

$$ y = |x - h| + k $$

Answer:

Based on the shapes of the graphs:

1. First Graph (Horizontal Line): Constant Function (e.g., \(y = 3\))
2. Second Graph (Curve with vertical asymptote at \(x=0\)): Logarithmic Function (e.g., \(y = \log(x)\))
3. Third Graph (V-shape): Absolute Value Function (e.g., \(y = |x + 5|\))