What are the domain and range of the polynomial y=25x2−4?(1 point)

Question

Responses

Domain: (−∞, ∞); Range: [−4, ∞)
Domain: open paren negative infinity comma infinity close paren ; Range: left bracket negative 4 comma infinity right parenthesis

Domain: [−4, ∞); Range: (−∞, ∞)
Domain: left bracket negative 4 comma infinity right parenthesis ; Range: open paren negative infinity comma infinity close paren

Domain: (−∞, ∞)
; Range: (−∞, −4]
Domain: (−∞, ∞)
; Range: left parenthesis negative infinity comma negative 4 right bracket

Domain: (−∞, ∞); Range: [0.4, ∞)

Answer 1

To determine the domain and range of the polynomial \( y = 25x^2 - 4 \):

1. Domain: The domain of a polynomial function is all real numbers since there are no restrictions (like square roots or divisions by zero). Therefore, the domain is \( (-\infty, \infty) \).

2. Range: The range of the quadratic function can be found by analyzing its vertex and direction. Since the coefficient of \( x^2 \) (which is 25) is positive, the parabola opens upwards. The vertex of the function is at \( y = -4 \) (the minimum value). Therefore, the range extends from the minimum \( -4 \) to infinity.

Thus, the range is \( [-4, \infty) \).

Final Answer:

• Domain: \( (-\infty, \infty) \)
• Range: \( [-4, \infty) \)

Therefore, the correct response is: Domain: (−∞, ∞); Range: [−4, ∞)