Consider the function

If necessary, give answers as fractions in simplest for. For example: -3/2

Find the following.

**(a) h(5) = Answer 1 Question 12** 


**(b) h(3) = Answer 2 Question 12** 


**(c) h(0) =Answer 3 Question 12** 

**(d) h(1/2) = Answer 4 Question 12** 

You didn't specify the function, but I’ll assume it's the same function as before:

\[
h(x) = \frac{2x + 1}{x + 5}
\]

If this is correct, let's proceed to find the values for the given inputs.

### **(a) Finding \( h(5) \):**

Substitute \( x = 5 \) into the function:

\[
h(5) = \frac{2(5) + 1}{5 + 5} = \frac{10 + 1}{10} = \frac{11}{10}
\]

So, the answer to **(a)** is:

\[
\boxed{\frac{11}{10}}
\]

### **(b) Finding \( h(3) \):**

Substitute \( x = 3 \) into the function:

\[
h(3) = \frac{2(3) + 1}{3 + 5} = \frac{6 + 1}{8} = \frac{7}{8}
\]

So, the answer to **(b)** is:

\[
\boxed{\frac{7}{8}}
\]

### **(c) Finding \( h(0) \):**

Substitute \( x = 0 \) into the function:

\[
h(0) = \frac{2(0) + 1}{0 + 5} = \frac{1}{5}
\]

So, the answer to **(c)** is:

\[
\boxed{\frac{1}{5}}
\]

### **(d) Finding \( h\left(\frac{1}{2}\right) \):**

Substitute \( x = \frac{1}{2} \) into the function:

\[
h\left(\frac{1}{2}\right) = \frac{2\left(\frac{1}{2}\right) + 1}{\frac{1}{2} + 5} = \frac{1 + 1}{\frac{1}{2} + \frac{10}{2}} = \frac{2}{\frac{11}{2}} = 2 \times \frac{2}{11} = \frac{4}{11}
\]

So, the

Consider the function If necessary, give answers as fractions in simplest form. For example: -3/2 Find the following. (a) h(5) = Answer 1 Question 12 (b) h(3) = Answer 2 Question 12 (c) h(0) = Answer 3 Question 12 (d) h(1/2) = Answer 4 Question 12

Learn how to evaluate the rational function h(x) = (2x + 1) / (x + 5) at various values such as 5, 3, 0, and 1/2. This problem involves substitution and simplification, and is suitable for students in Grades 9-11.

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