Function or Not a Function

Question

4x+53=y

y=8xsquared

Answer 1

To determine whether the given equations represent functions, we can analyze them based on the definition of a function: each input (x-value) must have exactly one output (y-value).

1. Equation: \( 4x + 53 = y \)

   This equation can be rewritten as: \[ y = 4x + 53 \] This is a linear equation in slope-intercept form (y = mx + b). For any input \( x \), there is exactly one corresponding output \( y \). Therefore, this equation is a function.

2. Equation: \( y = 8x^2 \)

   This equation represents a quadratic function. For any input \( x \), there is also exactly one output \( y \) since squaring any real number results in a single real number. Thus, this equation is also a function.

In summary:

• \( 4x + 53 = y \) is a function.
• \( y = 8x^2 \) is also a function.