Consider the following function. $$ f(x)=\left\{\begin{array}{rrr}5 x-2 & \text { if } & x=1 \ x^{2}+1 & \text { if } & 15 x

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Consider the following function. $$ f(x)=\left\{\begin{array}{rrr}5 x-2 & \text { if } & x=1 \ x^{2}+1 & \text { if } & 15 x<11 \ 7 & \text { if } & x \geq 11\end{array}\right. $$ Which "piece(s)" should be used to find the $$ y $$-intercept? Select all that apply. $$ \square $$ A. 7 $$ \square $$ B. $$ x^{2}+1 $$ $$ \square $$ C. $$ 5 x-2 $$

UpStudy AI · Accepted Answer

For the $$ y $$-intercept we need the value of $$ f(0) $$.

1. First, note that the $$ y $$-intercept occurs when $$ x=0 $$.

2. Check the conditions of the piecewise function:
   - The first piece applies only when $$ x=1 $$, so it does not apply for $$ x=0 $$.
   - The second piece applies when $$ 15x < 11 $$. Solving for $$ x $$:
     $$
     15x < 11 \implies x < \frac{11}{15}
     $$
     Since $$ 0 < \frac{11}{15} $$, the condition is satisfied.
   - The third piece applies when $$ x \geq 11 $$, which is not the case when $$ x=0 $$.

3. Therefore, for $$ x=0 $$, only the second piece $$ x^2+1 $$ applies.

Thus, the correct piece to use for finding the $$ y $$-intercept is:

$$ \square $$ B. $$ x^2+1 $$
To find the $$ y $$-intercept, use the piece $$ x^2 + 1 $$.

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