Question

Write each equation using function notation.

1. y − 2x = 5

2. y − 3x = 8x − 10

3. 2y + 6x = 10

4. −x2 = 7 − y

Answer 1

Answer:

1. f(x) = 2x + 5

2. f(x) = 11x - 10

3. f(x) = 5 - 3x

4. f(x) = x² + 7

Step-by-step explanation:

The function notation of the equation is f(x) = y

Put each equation in the form y = terms of x ± numerical terms, then change y to f(x)

1.

∵ The equation is y - 2x = 5

- Add 2x to both sides

∴ y = 2x + 5

∵ f(x) = y

∴ f(x) = 2x + 5

2.

∵ The equation is y - 3x = 8x - 10

- Add 3x to both sides

∴ y = 8x + 3x - 10

- Add the like terms in the right hand side

∴ y = 11x - 10

∵ f(x) = y

∴ f(x) = 11x - 10

3.

∵ The equation is 2y + 6x = 10

- Subtract 6x from both sides

∴ 2y = 10 - 6x

- Divide both sides by 2

∴ y = 5 - 3x

∵ f(x) = y

∴ f(x) = 5 - 3x

4.

∵ The equation is -x² = 7 - y

- Add y to both sides

∴ y - x² = 7

- Add x² to both sides

∴ y = x² + 7

∵ f(x) = y

∴ f(x) = x² + 7