Consider the function

h(x)= -2x/x+1

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** 

The function provided is \( h(x) = \frac{-2x}{x + 1} \).

Let's calculate the values for each part:

### (a) \( h(5) \)
\[
h(5) = \frac{-2(5)}{5 + 1} = \frac{-10}{6} = \frac{-5}{3}
\]
So, \( h(5) = \frac{-5}{3} \).

### (b) \( h(3) \)
\[
h(3) = \frac{-2(3)}{3 + 1} = \frac{-6}{4} = \frac{-3}{2}
\]
So, \( h(3) = \frac{-3}{2} \).

### (c) \( h(0) \)
\[
h(0) = \frac{-2(0)}{0 + 1} = \frac{0}{1} = 0
\]
So, \( h(0) = 0 \).

### (d) \( h\left(\frac{1}{2}\right) \)
\[
h\left(\frac{1}{2}\right) = \frac{-2\left(\frac{1}{2}\right)}{\frac{1}{2} + 1} = \frac{-1}{\frac{3}{2}} = \frac{-1 \times 2}{3} = \frac{-2}{3}
\]
So, \( h\left(\frac{1}{2}\right) = \frac{-2}{3} \).

### Summary:
- (a) \( h(5) = \frac{-5}{3} \)
- (b) \( h(3) = \frac{-3}{2} \)
- (c) \( h(0) = 0 \)
- (d) \( h\left(\frac{1}{2}\right) = \frac{-2}{3} \)

Would you like further explanation on any part of the process?

Here are 5 related questions to explore:
1. What is the domain of the function \( h(x) = \frac{-2x}{x+1} \)?
2. What is the range of \( h(x) \) based on its expression?
3. Can you find the vertical asymptote of the function \( h(x) \)?
4. How would you calculate \( h(x) \) when \( x = -1 \)?
5. How does \( h(x) \) behave as \( x \) approaches infinity?

**Tip:** Always simplify fractions by dividing both the numerator and denominator by their greatest common factor!

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

Learn how to evaluate the rational function h(x) = -2x / (x + 1) at different values of x. This solution includes step-by-step calculations for h(5), h(3), h(0), and h(1/2), covering core concepts in algebra and rational expressions. Suitable for students in Grades 8-10.

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