Mathematics for Management -- Supplementary Electronic Materials

Quiz: The Graph of a Function

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1. In a function how many different outputs can a single input have?

infinite one zero two

2. Which relation is a function?

\( \begin{array}{c || c c c c} x & 3 & 5 & 3 & 9 \\ \hline y & 8 & 10 & 6 & -2 \end{array} \) \( \begin{array}{c || c c c c} x & 3 & 5 & 6 & 9 \\ \hline y & 8 & 10 & 6 & -2 \end{array} \) \( \begin{array}{c || c c c c} x & 3 & 5 & 6 & 5 \\ \hline y & 8 & 10 & 6 & -2 \end{array} \) \( \begin{array}{c || c c c c} x & 6 & 5 & 6 & 9 \\ \hline y & 8 & 10 & 6 & -2 \end{array} \)

3. Evaluate the following piecewise function \(f(x)\) at the value \(x = 2\). \[ f(x) \, \, = \, \, \left\{ \begin{array}{l c l} 3x + 1 \, , & & \text{if \(x < -1\)} \\[1mm] -2x - 5 \, , & & \text{if \(x \geq -1\)} \end{array} \right. \]

\( -9 \) \( -8 \) \( -3 \) \( 1 \)

4. Given the following piecewise function \(f(x)\) what is its range? (Hint: draw the graph.) \[ f(x) \, \, = \, \, \left\{ \begin{array}{l c l} 4 \, , & & \text{if \(-5 \leq x < -2\)} \\[1mm] |x| \, , & & \text{if \(-2 \leq x < 8\)}\\[1mm] \sqrt{x} \, , & & \text{if \(8 \leq x \leq 13\)} \end{array} \right. \]

\( [0, \infty) \) \( [-2, 8] \) \( [0, \sqrt{13}] \) \( [0, 8] \)

5. Let \(f_1(x) = x^2 - x + k\) and \(f_2(x) = -x-5\). For which value of \(k\) do the intersection points \((x,y)\) of the graph of these two functions have the \(x\)-coordinates \(-1\) and \(1\).

\( k = 6 \) \( k = -6 \) \( k = -5 \) \( k = 5 \)

6. Let two quadratic functions be given by \(y = x^2 + x - 2\) and \(y = a(x^2 + x - 2)\) with \(a \neq 0, 1\). Then, which of the following statements is true?

the functions do not intersect the functions intersect at one location only the functions intersect at two locations the functions intersect at more than two locations

7. Which are the \(x\)- and \(y\)- intercept points of the quadratic function \(f(x) = -3(x+2)(x-3)\)?

\(x\)-intercept: \((-2,0)\), \((3,0)\); \(y\)-intercept: \((0,18) \) \(x\)-intercept: \((-2,0)\), \((3,0)\); \(y\)-intercept: \((0,-18)\) \(x\)-intercept: \((2,0)\), \((-3,0)\); \(y\)-intercept: \((0,18)\) \(x\)-intercept: \((2,0)\), \((-3,0)\); \(y\)-intercept: \((0,-18)\)

8. If a circle with a diameter of \(10.4\) units were to be drawn in the coordinate plane with its center at the origin, what are be the coordinates of its \(x\)- and \(y\)-intercept points?

\((5.2, 0)\), \((0, 5.2) \) \((-5.2, 0)\), \((5.2, 0)\), \((0, -5.2)\), \((0, 5.2)\) \((-10.4, 0)\), \((10.4, 0)\), \((0, -10.4)\), \((0, 10.4)\) \((10.4,0)\), \((0, 10.4)\)

9. Identify the maximum or minimum value and the domain and range of the graph of the function \(y = 2 (x+2)^2 - 3\).

minimum value: 3, domain: \([3, \infty)\), range: \(\mathbb{R}\) maximum value: -3, domain: \((-\infty, -3]\), range: \(\mathbb{R} \) maximum value: 3, domain: \(\mathbb{R}\), range: \((-\infty, 3] \) minimum value: -3, domain: \(\mathbb{R}\), range: \([-3, \infty) \)

10. Given the quadratic function \(f(x) = -2x^2 - 20x - 48\), determine which of the following is/are true:

I) The graph's maximum value occurs at \(x = -5\).
II) The \(x\)-intercepts of the function occur at \(x = -6\) and \(x = -4\).
III) The \(y\)-intercept of the function is located at \((0, -24)\).

only I) is true only I) and II) are true only III) is true all are true

Your grade is: __ of 10

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Solution: 1b; 2b; 3a; 4d; 5b; 6b; 7a; 8b; 9d; 10b

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.