Question

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Explanation:

Identify the functions and their transformations

Using the Square Root Function and Function Transformations knowledge points, we analyze the general form of a transformed square root function starting at the origin:

$$ y = a\sqrt{x} $$

where \(a > 0\) represents a vertical stretch or compression.

• The green curve passes through \((-1, 3)\) when reflected, or more standardly, if we look at the grid where the y-axis is the vertical line with \(5\) marked:
• The vertex of all three functions is at \((0, 0)\) (or they are reflected horizontally as \(y = a\sqrt{-x}\)).
• Let's find the value of \(a\) for each curve by identifying a clear point on each graph:
• For the green curve, at \(x = -1\), the value is \(y = 3\). Thus, \(3 = a\sqrt{-(-1)} \implies a = 3\).
• For the blue curve (the middle one, standard curve), at \(x = -1\), the value is \(y = 1\). Thus, \(1 = a\sqrt{-(-1)} \implies a = 1\).
• For the red curve (the lowest one, compressed vertically), at \(x = -9\), the value is \(y = 1\). Thus, \(1 = a\sqrt{-(-9)} \implies 1 = 3a \implies a = \frac{1}{3}\).

Match the items

Using the Vertical Stretch knowledge point:

• Green function: \(a = 3\) (corresponds to item b)
• Red function: \(a = 1/3\) (corresponds to item c)
• Blue function: \(a = 1\) (corresponds to item a)

Answer:

1. Green function: b (3)
2. Red Function: c (1/3)
3. Blue function: a (1)