To evaluate the truth of the statements regarding the function \( f(x) = 12x + 32 \) and complete the table, we need to calculate \( f \) for the relevant \( x \) values mentioned in the options.
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Calculating \( f(2) \): \[ f(2) = 12(2) + 32 = 24 + 32 = 56 \]
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Calculating \( f(-\frac{1}{2}) \): \[ f(-\frac{1}{2}) = 12(-\frac{1}{2}) + 32 = -6 + 32 = 26 \]
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Calculating \( f(0) \): \[ f(0) = 12(0) + 32 = 0 + 32 = 32 \]
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Calculating \( f(1) \): \[ f(1) = 12(1) + 32 = 12 + 32 = 44 \]
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Calculating \( f(4) \): \[ f(4) = 12(4) + 32 = 48 + 32 = 80 \]
Now let's evaluate the statements:
- f(2)=1: False (as \( f(2) = 56 \))
- f(-\frac{1}{2})=-2: False (as \( f(-\frac{1}{2}) = 26 \))
- f(0)=32: True (as \( f(0) = 32 \))
- f(1)=-1: False (as \( f(1) = 44 \))
- f(4)=72: False (as \( f(4) = 80 \))
True statements:
- \( f(0) = 32 \)
Therefore, the only true statement is:
- f(0)=32
It appears I need to correct or double-check more options to find additional correct statements, as requested to find two. Based on the calculated values and the original options given, it seems that the first analysis mainly returned one true statement.
If you have options and results expected that indicate something different, please check the values or clarify for any calculations to be retaken.
Correct identification based on these:
- Therefore, the initially evaluated "true statement" is noted, but a consideration from the evaluative range allows room for verification on calculations or original structure towards two points needed.
Further clarifications will point out likely missed statements or adjustments; hence, feel free to provide updates for adjustive knowledge based on the evaluated function.