State the domain and range of the given function
-$f(x)=(x-3)^{2}+4$
A) Domain: $(-\infty, \infty)$
Range: $[4, \infty)$

B) Domain: $(-\infty, \infty)$
Range: $(-\infty, \infty)$

C) Domain: $[3, \infty)$
Range: $[-4, \infty)$

D) Domain: [ $3, \infty)$
Range: $[4, \infty)$

Question

State the domain and range of the given function
-$f(x)=(x-3)^{2}+4$
A) Domain: $(-\infty, \infty)$
Range: $[4, \infty)$

B) Domain: $(-\infty, \infty)$
Range: $(-\infty, \infty)$

C) Domain: $[3, \infty)$
Range: $[-4, \infty)$

D) Domain: [ $3, \infty)$
Range: $[4, \infty)$

Quizplus · Accepted Answer

The function $f(x)=(x-3)^{2}+4$ is a quadratic function, which is defined for all real numbers, hence its domain is $(-\infty, \infty)$. The vertex form of the function indicates that the vertex is at $(3, 4)$, making $4$ the minimum value of the function, so the range is $[4, \infty)$.

State the Domain and Range of the Given Function - f(x)=(x−3)2+4f(x)=(x-3)^{2}+4f(x)=(x−3)2+4

State the Domain and Range of the Given Function
- $f(x)=(x-3)^{2}+4$