$$ f(x)=\left\{\begin{array}{ll}4+2 x & ext { if } x

Question

$$ f(x)=\left\{\begin{array}{ll}4+2 x & 	ext { if } x<0 \ x^{2} & 	ext { if } x \geq 0\end{array}ight. $$ The function $$ f $$ is defined as follows. (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (a) The domain of the function $$ f $$ is (Type your answer in interval notation.)

UpStudy AI · Accepted Answer

**Step 1. Analyze the definition of $$ f(x) $$**

The function $$ f(x) $$ is defined in two pieces:
- For $$ x < 0 $$: $$ f(x) = 4 + 2x $$
- For $$ x \geq 0 $$: $$ f(x) = x^2 $$

**Step 2. Determine the domain**

Since both pieces are defined for all values within their respective intervals:
- $$ 4 + 2x $$ is defined for all $$ x < 0 $$
- $$ x^2 $$ is defined for all $$ x \geq 0 $$

There is no value of $$ x $$ where $$ f(x) $$ is left undefined.

**Final Answer:**

The domain of $$ f $$ is $$(-\infty, \infty)$$.
The domain of $$ f $$ is all real numbers, written as $$(-\infty, \infty)$$.

The function is defined as follows.
(a) Find the domain of the function.
(b) Locate any intercepts.
© Graph the function.
(d) Based on the graph, find the range.
(a) The domain of the function is
(Type your answer in interval notation.)

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The function is defined as follows. (a) Find the domain of the function. (b) Locate any intercepts. © Graph the function. (d) Based on the graph, find the range. (a) The domain of the function is (Type your answer in interval notation.)