# Download PDF by Marcel B. Finan: A Reform Approach to Business Calculus

By Marcel B. Finan

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What about k < 0? If |k| > 1 then the graph of kf (x) is a vertical stretch of the graph of f (x) followed by a reflection about the x-axis. If 0 < |k| < 1 then the graph of kf (x) is a vertical compression of the graph of f (x) by a factor of k followed by a reflection about the x-axis. Horizontal Stretches and Compressions: If a function f (x) is given, then the graph of f (kx) is a horizontal stretch of the graph of f (x) by a factor of k1 for 0 < k < 1, and a horizontal compression for k > 1.

DC is measured in dollars per gallon. 4 dollars. 2 The derivative of the velocity function v is called acceleration and is denoted by a. Suppose that v is measured in meters/seconds, what are the units of a? Solution. The units of a are meters/seconds/seconds = meters/seconds2 . Local Linear Approximation Finally, one can use the derivative at a point to approximate values of the function at nearby points. For example, if we know the values of f (a) and f (a) then for a nearby point b the value of f (b) is found by the formula f (b) ≈ f (a)(b − a) + f (a).

Figure 18 Shows the graph of sin x and Figure 19 shows the graph of cos x. Figure 18 Figure 19 53 Amplitude and period of y = a sin (bx), y = a cos (bx), b > 0 We now consider graphs of functions that are transformations of the sine and cosine functions. e. the y values). Since −1 ≤ sin (bx) ≤ 1 and −1 ≤ cos (bx) ≤ 1 then −a ≤ a sin (bx) ≤ a and −a ≤ a cos (bx) ≤ a. So, the range of the function y = a sin (bx) or the function y = a cos (bx) is the closed interval [−a, a]. The number |a| is called the amplitude.