Questions: A telephone company offers a monthly cellular phone plan for 40.00. It includes 350 free minutes plus 0.25 per minute for additional minutes. The following function gives the monthly cost for a subscriber, where x is the number of minutes used. C(x)= 40.00 if 0 ≤ x ≤ 350 40.00+0.25(x-350) if x>350 Simplify the expression in the second line of the piecewise function. Then use point-plotting to graph the function Fill in the simplified expression below. C(x)= 40.00 if 0 ≤ x ≤ 350 if x>350 (Use integers or decimals for any numbers in the expression. Do not factor.)

A telephone company offers a monthly cellular phone plan for 40.00. It includes 350 free minutes plus 0.25 per minute for additional minutes. The following function gives the monthly cost for a subscriber, where x is the number of minutes used. C(x)= 40.00 if 0 ≤ x ≤ 350 40.00+0.25(x-350) if x>350 Simplify the expression in the second line of the piecewise function. Then use point-plotting to graph the function Fill in the simplified expression below. C(x)= 40.00 if 0 ≤ x ≤ 350 if x>350 (Use integers or decimals for any numbers in the expression. Do not factor.)
Transcript text: A telephone company offers a monthly cellular phone plan for $\$ 40.00$. It includes 350 free minutes plus $\$ 0.25$ per minute for additional minutes. The following function gives the monthly cost for a subscriber, where x is the number of minutes used. \[ C(x)=\left\{\begin{array}{ll} 40.00 & \text { if } 0 \leq x \leq 350 \\ 40.00+0.25(x-350) & \text { if } x>350 \end{array}\right. \] Simplify the expression in the second line of the piecewise function. Then use point-plotting to graph the function Fill in the simplified expression below. \[ C(x)=\left\{\begin{array}{ll} 40.00 & \text { if } 0 \leq x \leq 350 \\ \square & \text { if } x>350 \end{array}\right. \] (Use integers or decimals for any numbers in the expression. Do not factor.)
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Solution

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Solution Steps

Step 1: Simplify the Expression

The given piecewise function is:

\[ C(x)=\left\{\begin{array}{ll} 40.00 & \text { if } 0 \leq x \leq 350 \\ 40.00+0.25(x-350) & \text { if } x>350 \end{array}\right. \]

To simplify the expression in the second line, distribute the \(0.25\) and combine like terms:

\[ 40.00 + 0.25(x - 350) = 40.00 + 0.25x - 87.50 = 0.25x - 47.50 \]

Final Answer

The simplified piecewise function is:

\[ C(x)=\left\{\begin{array}{ll} 40.00 & \text { if } 0 \leq x \leq 350 \\ 0.25x - 47.50 & \text { if } x>350 \end{array}\right. \]

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 500, "ymin": 0, "ymax": 100}, "commands": ["y = 40", "y = 0.25x - 47.50"], "latex_expressions": ["$C(x) = 40$", "$C(x) = 0.25x - 47.50$"]}

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