Questions: Evaluate the following function at the indicated values. H(x)=2^x (a) H(-4) (b) H(0) (c) H(5)

Evaluate the following function at the indicated values. H(x)=2^x (a) H(-4) (b) H(0) (c) H(5)
Transcript text: Evaluate the following function at the indicated values. \[ H(x)=2^{x} \] (a) $H(-4)$ (b) $H(0)$ (c) $H(5)$
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Solution

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Solution Steps

To evaluate the function \( H(x) = 2^x \) at the given values, we simply need to substitute the values of \( x \) into the function and compute the result.

Step 1: Evaluate \( H(-4) \)

To find \( H(-4) \), we substitute \( x = -4 \) into the function: \[ H(-4) = 2^{-4} = \frac{1}{2^4} = \frac{1}{16} = 0.0625 \]

Step 2: Evaluate \( H(0) \)

Next, we evaluate \( H(0) \): \[ H(0) = 2^0 = 1 \]

Step 3: Evaluate \( H(5) \)

Finally, we calculate \( H(5) \): \[ H(5) = 2^5 = 32 \]

Final Answer

The results for each evaluation are:

  • \( H(-4) = 0.0625 \)
  • \( H(0) = 1 \)
  • \( H(5) = 32 \)

Thus, the final answers are: \[ \boxed{H(-4) = 0.0625}, \quad \boxed{H(0) = 1}, \quad \boxed{H(5) = 32} \]

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