Unlock the Power of Variable Multiplication in Math: Understanding the Equation y = af(x) with a > 1

y=af(x) a>1

In the given equation, y = af(x), where a > 1, we have a variable “x” being passed into the function f(x)

In the given equation, y = af(x), where a > 1, we have a variable “x” being passed into the function f(x). The function f(x) is then multiplied by a positive constant “a” to obtain the output y.

Here is a step-by-step explanation of the equation:

1. Choose a value for x: Start by selecting a numerical value for x. This can be any real number.

2. Evaluate f(x): Substitute the chosen value of x into the function f(x) to obtain a corresponding output value. For example, if f(x) = 2x, and you chose x = 3, then f(3) = 2(3) = 6.

3. Multiply f(x) by a: Take the output value obtained in step 2 and multiply it by the constant “a”. This will give you the final value of y. Since a > 1, multiplying f(x) by a increases the magnitude of the output.

Let’s illustrate this with an example:

Suppose we have y = 3f(x), where f(x) = x^2, and we choose x = 2.

Step 1: Choose a value for x: x = 2

Step 2: Evaluate f(x): Substitute x = 2 into f(x): f(2) = (2)^2 = 4

Step 3: Multiply f(x) by a: Multiply the result from step 2 by a = 3: y = 3 * 4 = 12

Therefore, for x = 2, y would be equal to 12 in this scenario.

Remember, the value of a > 1 means that y will be greater than f(x) alone. This multiplication by a amplifies the effect of f(x) on the output y.

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