QuestionConsider the following function. $f(x)=\left\{\begin{array}{rlr} 5 x-4 & \text { if } & x<2 \\ x^{2}+5 & \text { if } & 2 \leq x<9 \\ 3 & \text { if } & x \geq 9 \end{array}\right.$
Which "piece(s)" should be used to find the $y$ -intercept?
Select all that apply. A. 3 B. $5 x-4$ C. $x^{2}+5$

Studdy Solution

STEP 1

1. The function $f(x)$ is a piecewise function with three different expressions depending on the value of $x$ .
2. The $y$ -intercept of a function is the point where the graph of the function crosses the $y$ -axis, which occurs when $x = 0$ .

STEP 2

1. Identify the condition for each piece of the piecewise function.
2. Determine which piece is applicable when $x = 0$ .

STEP 3

Identify the condition for each piece of the piecewise function:
- The first piece $5x - 4$ is used when $x < 2$ . - The second piece $x^2 + 5$ is used when $2 \leq x < 9$ . - The third piece $3$ is used when $x \geq 9$ .

STEP 4

Determine which piece is applicable when $x = 0$ :
Since $0 < 2$ , we use the first piece $5x - 4$ .
The piece that should be used to find the $y$ -intercept is $\boxed{5x - 4}$ , which corresponds to option B.

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