91Ó°ÊÓ

Horizontal shifts, vertical shifts, and reflections are called ________ transformations.

The points at which a graph intersects or touches an axis are called the ________ of the graph.

For each function, sketch (on the same set of coordinate axes) a graph of each function for \(c = -1\), \(1\), and \(3\). (a) \(f(x) = |x| + c\) (b) \(f(x) = |x - c|\) (c) \(f(x) = |x + 4| + c\)

In Exercises 7-14, determine whether each point lies on the graph of the equation. \( y = \sqrt{x+4} \) (a) \( (0, 2) \) (b) \( (5, 3) \)

In Exercises 1-9, match each function with its name. \(f(x) = |x|\) (a) squaring function (b) square root function (c) cubic function (d) linear function (e) constant function (f) absolute value function (g) greatest integer function (h) reciprocal function (i) identity function

Match each equation of a line with its form. (a) \( Ax + By + C = 0 \) (b) \( x = a \) (c) \( y = b \) (d) \( y = mx + b \) (e) \( y - y_1 = m(x-x_1) \) (i) Vertical line (ii) Slope-intercept form (iii) General form (iv) Point-slope form (v) Horizontal line

In Exercises 1-9, match each function with its name. \(f(x) = x^3\) (a) squaring function (b) square root function (c) cubic function (d) linear function (e) constant function (f) absolute value function (g) greatest integer function (h) reciprocal function (i) identity function

In Exercises 7-10, plot the points in the Cartesian plane. \( (3, 8) \), \( (0.5, -1) \), \( (5, -6) \), \( (-2, 2.5) \)

In Exercises 7-14, find the inverse function of \(f\) informally. Verify that \(f(f^{-1}(x)) = x\) and \(f^{-1}(f(x)) = x\). \(f(x) = x - 4\)

SPORTS The winning times (in minutes) in the women's 400-meter freestyle swimming event in the Olympics from 1948 through 2008 are given by the following ordered pairs. \((1948, 5.30)\) \((1952, 5.20)\) \((1956, 4.91)\) \((1960, 4.84)\) \((1964, 4.72)\) \((1968, 4.53)\) \((1972, 4.32)\) \((1976, 4.16)\) \((1980, 4.15)\) \((1984, 4.12)\) \((1988, 4.06)\) \((1992, 4.12)\) \((1996, 4.12)\) \((2000, 4.10)\) \((2004, 4.09)\) \((2008, 4.05)\) A linear model that approximates the data is \(y = -0.020t + 5.00\), where \(y\) represents the winning time (in minutes) and \(t=0\) represents 1950. Plot the actual data and the model on the same set of coordinate axes. How closely does the model represent the data? Does it appear that another type of model may be a better fit? Explain. (Source: International Olympic Committee)