Which of the following piecewise functions is continuous at $x = 0$?
Question 2
A tax system has the following rules: income up to $$ \$20,000$ is taxed at $10\%$; income over $ \$20,000$ and up to $ \$50,000$ is taxed at $15\%$; and income over $ \$50,000$ is taxed at $20\%$. Which piecewise function represents the tax $T(x)$ on an income of $x$$ dollars?
Question 3
Given the piecewise function $$f(x) = \begin{cases} x^2 - 3 & \text{if } x < -1 \\ 2x + 1 & \text{if } -1 \le x < 2 \\ 5 - x & \text{if } x \ge 2 \end{cases}$$, what is the value of $f(2)$?
Question 4
Consider the piecewise function $f(x) = \begin{cases} ax + 2 & \text{if } x < 1 \\ x^2 - 3x + 5 & \text{if } x \ge 1 \end{cases}$. For what value of $a$ is the function continuous at $x = 1$?
Question 5
Which of the following graphs represents a piecewise function with a discontinuity at $x = 1$?
