determine for what numbers, if any, the given function is discontinuous. f(x)=6x² + 4x + 4 select the…
determine for what numbers, if any, the given function is discontinuous. f(x)=6x² + 4x + 4 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function f is discontinuous at (use a comma to separate answers as needed.) b. the function f is continuous everywhere.
Answer
Explanation:
Step1: Recall continuity definition
A polynomial function $y = a_nx^n+\cdots+a_1x + a_0$ is continuous at every real - number $x = c$ if $\lim_{x\rightarrow c}f(x)=f(c)$.
Step2: Identify function type
The given function $f(x)=6x^{2}+4x + 4$ is a polynomial function of degree 2 (quadratic function), where $a_2 = 6$, $a_1=4$, and $a_0 = 4$.
Step3: Determine continuity
Polynomial functions are continuous for all real numbers. That is, for any real number $c$, $\lim_{x\rightarrow c}(6x^{2}+4x + 4)=6c^{2}+4c + 4=f(c)$.
Answer:
B. The function f is continuous everywhere.