{"id":15284,"date":"2021-10-11T22:48:53","date_gmt":"2021-10-11T22:48:53","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/functions-practice-test\/"},"modified":"2021-10-25T03:12:30","modified_gmt":"2021-10-25T03:12:30","slug":"functions-practice-test","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/functions-practice-test\/","title":{"raw":"Functions Practice Test","rendered":"Functions Practice Test"},"content":{"raw":"For the following exercises, determine whether each of the following relations is a function.\r\n\r\n1. y\u00a0<\/em>= 2x\u00a0<\/em>+ 8\r\n\r\n2. [latex]\\left\\{\\left(2,1\\right),\\left(3,2\\right),\\left(-1,1\\right),\\left(0,-2\\right)\\right\\}[\/latex]\r\n\r\nFor the following exercises, evaluate the function [latex]f\\left(x\\right)=-3{x}^{2}+2x[\/latex]\u00a0at the given input.\r\n\r\n3. [latex]f\\left(-2\\right)[\/latex]\r\n\r\n4.\u00a0[latex]f\\left(a\\right)[\/latex]\r\n\r\n5. Show that the function [latex]f\\left(x\\right)=-2{\\left(x - 1\\right)}^{2}+3[\/latex] is not one-to-one.\r\n\r\n6.\u00a0Write the domain of the function [latex]f\\left(x\\right)=\\sqrt{3-x}[\/latex] in interval notation.\r\n\r\n7. Given [latex]f\\left(x\\right)=2{x}^{2}-5x[\/latex], find [latex]f\\left(a+1\\right)-f\\left(1\\right)[\/latex].\r\n\r\n8.\u00a0Graph the function [latex]\\begin{cases}f\\left(x\\right) & =x+1 & \\text{ if }-2 < x < 3 \\\\ \\text{ }& =-x & \\text{ if }x\\ge 3\\end{cases}[\/latex]\r\n\r\nFor the following exercises, use the graph of the piecewise-defined function shown below.\r\n\"Graph\r\n\r\n9.\u00a0Find [latex]f\\left(2\\right)[\/latex].\r\n\r\n10.\u00a0Find [latex]f\\left(-2\\right)[\/latex].\r\n\r\nFor the following exercises, use the values listed below.<\/span>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
x<\/strong><\/em><\/td>\r\nF<\/strong><\/em>(x<\/em>)<\/strong><\/td>\r\n<\/tr>\r\n
0<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n9<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n11<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n13<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n15<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n17<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n11. Solve the equation [latex]F\\left(x\\right)=5[\/latex].\r\n\r\n12. Find [latex]F\\left(6\\right)[\/latex].\r\n\r\n13. Is the function represented by the table one-to-one?\r\n\r\nSee the next page for the solutions\u00a0to the odd-numbered problems.<\/em><\/span>","rendered":"

For the following exercises, determine whether each of the following relations is a function.<\/p>\n

1. y\u00a0<\/em>= 2x\u00a0<\/em>+ 8<\/p>\n

2. [latex]\\left\\{\\left(2,1\\right),\\left(3,2\\right),\\left(-1,1\\right),\\left(0,-2\\right)\\right\\}[\/latex]<\/p>\n

For the following exercises, evaluate the function [latex]f\\left(x\\right)=-3{x}^{2}+2x[\/latex]\u00a0at the given input.<\/p>\n

3. [latex]f\\left(-2\\right)[\/latex]<\/p>\n

4.\u00a0[latex]f\\left(a\\right)[\/latex]<\/p>\n

5. Show that the function [latex]f\\left(x\\right)=-2{\\left(x - 1\\right)}^{2}+3[\/latex] is not one-to-one.<\/p>\n

6.\u00a0Write the domain of the function [latex]f\\left(x\\right)=\\sqrt{3-x}[\/latex] in interval notation.<\/p>\n

7. Given [latex]f\\left(x\\right)=2{x}^{2}-5x[\/latex], find [latex]f\\left(a+1\\right)-f\\left(1\\right)[\/latex].<\/p>\n

8.\u00a0Graph the function [latex]\\begin{cases}f\\left(x\\right) & =x+1 & \\text{ if }-2 < x < 3 \\\\ \\text{ }& =-x & \\text{ if }x\\ge 3\\end{cases}[\/latex]\n\nFor the following exercises, use the graph of the piecewise-defined function shown below.\n\"Graph<\/p>\n

9.\u00a0Find [latex]f\\left(2\\right)[\/latex].<\/p>\n

10.\u00a0Find [latex]f\\left(-2\\right)[\/latex].<\/p>\n

For the following exercises, use the values listed below.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
x<\/strong><\/em><\/td>\nF<\/strong><\/em>(x<\/em>)<\/strong><\/td>\n<\/tr>\n
0<\/td>\n1<\/td>\n<\/tr>\n
1<\/td>\n3<\/td>\n<\/tr>\n
2<\/td>\n5<\/td>\n<\/tr>\n
3<\/td>\n7<\/td>\n<\/tr>\n
4<\/td>\n9<\/td>\n<\/tr>\n
5<\/td>\n11<\/td>\n<\/tr>\n
6<\/td>\n13<\/td>\n<\/tr>\n
7<\/td>\n15<\/td>\n<\/tr>\n
8<\/td>\n17<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

11. Solve the equation [latex]F\\left(x\\right)=5[\/latex].<\/p>\n

12. Find [latex]F\\left(6\\right)[\/latex].<\/p>\n

13. Is the function represented by the table one-to-one?<\/p>\n

See the next page for the solutions\u00a0to the odd-numbered problems.<\/em><\/span><\/p>\n\n\t\t\t

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