91Ó°ÊÓ

In Exercises 15 and 16, which sets of ordered pairs represent functions from \(A\) to \(B\)? Explain. \(A = \\{0, 1, 2, 3\\}\) and \(B = \\{-2, -1, 0, 1, 2\\}\) (a) \(\\{(0, 1), (1, -2), (2, 0), (3, 2)\\}\) (b) \(\\{(0, -1), (2, 2), (1, -2), (3, 0), (1, 1)\\}\) (c) \(\\{(0, 0), (1, 0), (2, 0), (3, 0)\\}\) (d) \(\\{(0, 2), (3, 0), (1, 1)\\}\)

In Exercises 19-36, determine whether the equation represents \(y\) as a function of \(x\). \(x^2 + y^2 = 4\)

In Exercises 19-22, verify that \(f\) and \(g\) are inverse functions. \(f(x) = -\frac{7}{2}x - 3\), \(g(x) = -\frac{2x+6}{7}\)

In Exercises 19-22, graphically estimate the \( x \)- and \( y \)-intercepts of the graph. Verify your results algebraically. \( y = 16 - 4x^2 \)

In Exercises 25-54, \(g\) is related to one of the parent functions described in Section 1.6. (a) Identify the parent function \(f\). (b) Describe the sequence of transformations from \(f\) to \(g\). (c) Sketch the graph of \(g\). (d) Use function notation to write \(g\) in terms of \(f\). $$ g(x)=2(x-7)^{2} $$

In Exercises 25-54, \(g\) is related to one of the parent functions described in Section 1.6. (a) Identify the parent function \(f\). (b) Describe the sequence of transformations from \(f\) to \(g\). (c) Sketch the graph of \(g\). (d) Use function notation to write \(g\) in terms of \(f\). \(g (x) = -x^3 - 1\)

In Exercises 25-54, \(g\) is related to one of the parent functions described in Section 1.6. (a) Identify the parent function \(f\). (b) Describe the sequence of transformations from \(f\) to \(g\). (c) Sketch the graph of \(g\). (d) Use function notation to write \(g\) in terms of \(f\). \(g (x) = 2(x-7)^2 \)

In Exercises 33-40, use the algebraic tests to check for symmetry with respect to both axes and the origin. \( xy^2 + 10 = 0 \)

MEASUREMENT On a yardstick with scales in inches and centimeters, you notice that 13 inches is approximately the same length as 33 centimeters. Use this information to find a mathematical model that relates centimeters \(y\) to inches \(x\). Then use the model to find the numbers of centimeters in 10 inches and 20 inches.

In Exercises 37-52, evaluate the function at each specified value of the independent variable and simplify. \(g(t) = 4t^2-3t+5\) (a) \(g(2)\) (b) \(g(t-2)\) (c) \(g(t)-g(2)\)