Question

1. Use the following function rule to find (2). () = − 3

2. Use the following function rule to find (−3). () = 2 − 5
3. 3. Use the following function rule to find ( + 5). () = − 7
4. Use the following function rule to find ( − 9). () = + 12

Answer 1

To evaluate function rules at given values, substitute the values into the function and perform the arithmetic, taking the signs into account. For f(2) in -3x, f(2) = -6; for f(-3) in 2x - 5, f(-3) = -11; for f(x + 5) in -7x, f(x + 5) = -7x - 35; for f(x - 9) in x + 12, f(x - 9) = x + 3.

Step-by-step explanation:

Understanding Function Rules and Calculations

To solve for specific values using a function rule, you replace the variable with the given numbers and calculate the result. For each step, we will substitute the given value into the function and perform the calculation following the rules of arithmetic.

1. Find f(2) for the function f(x) = -3x. Substituting 2 for x, we get f(2) = -3(2) = -6.
2. Find f(-3) for the function f(x) = 2x - 5. Substituting -3 for x, we get f(-3) = 2(-3) - 5 = -6 - 5 = -11.
3. Find f(x + 5) for the function f(x) = -7x. To find this, we substitute (x + 5) for x, giving us f(x + 5) = -7(x + 5) = -7x - 35.
4. Find f(x - 9) for the function f(x) = x + 12. Substituting (x - 9) for x, we have f(x - 9) = (x - 9) + 12 = x + 3.

Remember, following the rules of signs is crucial for addition, subtraction, multiplication, and division. When adding or subtracting, the sign of the original numbers often determines the sign of the result. For multiplication and division, two like signs give a positive result, and two unlike signs give a negative result.