To find the equation of the square root function that Jonathan graphed, we need to analyze the given information. The given equation is in the form:
\[ y = \frac{1}{2} \sqrt{x} - \text{(some value)} \]
From your description, it seems that the graph starts at \( x = 4 \) and potentially goes up to \( 5, 6, 7, 8 \) on the y-axis.
To determine the missing value in the equation, we can substitute \( x = 4 \) into the equation to see what would be needed for \( y = 0 \), assuming that the graph starts from the x-axis (where \( y=0 \)):
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Plugging \( x = 4 \) into the equation: \[ y = \frac{1}{2} \sqrt{4} - b \] where \( b \) is the blank we need to fill.
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Since \( \sqrt{4} = 2 \), this simplifies to: \[ y = \frac{1}{2} \times 2 - b = 1 - b \]
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If the graph starts at \( y = 0 \) when \( x = 4 \): \[ 0 = 1 - b \] This means: \[ b = 1 \]
Putting everything together, the equation of the function Jonathan graphed is:
\[ y = \frac{1}{2} \sqrt{x} - 1 \]
This function has a starting point on the x-axis (where \( y = 0 \)) at \( x = 4 \). As \( x \) increases beyond 4, the value of \( y \) will increase as well.
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