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addition: (g + h)(x) = g(x) + h(x); subtraction: (g − h)(x) = g(x) − h(x) For instance, 2 can be multiplied by x by simply writing 2x;. A. gallons per hour The height, in feet, of the football above the ground h trinomial can be factored to obtain x (x + 2) (x – 1), which is. f(x+h)-f(x)/h is a formula that is a part of limit definition of the derivative (first principles). Example 1: Compute f(x+h)-f(x)/h when f(x) = 2x - 7.

1. 7) Given f(x) = x+1/x+4 ar and g(x): find (fog)(x). X. 8) Using transformations sketch a graph of the given functions: a) f(x)=(x-3)2 c) f(x) = √6−3x. Example 1: Sketch the graph of each function. (a) h (x) = x. 2. + 2. (b) g (x) = |x| – 3. Solution (a). Step 1: First, we determine which library function. Solve each problem using the methods demonstrated in class; be sure to answer word problems in a phrase or sentence. 1) Use a graphing calculator to graph.

Given f (x) = 2x – 5 and g (x) = 1 – x find (f – g) (x) and (f – g) (2). Solution. Step 1. Find (f – g) (x). (f – g) (x) = f. Finding an average rate of change is just finding the slope between 2 points. You can always find the slope. m = (y2-y1)/(x2-x1) The slope could be 0. h. This equation is essentially the old slope equation for a line: 1. 2. 1. 2 xx y y m. -. -. = f (x+h). – represents (y2) f (x). – represents (y1) x.

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For instance, h = f ◦ g. (1) h is the function that is made from f composed with g. For regular functions such as, say: f(x)=3x2 + 2x + 1. (2). Calculating and Interpreting the Slope of a Line. m=ΔyΔx=y2−y1x2−x1. We can interpret this equation by saying that the slope m m measures the change in y. y = 2x – 5, where the domain is {x|1 ≤ x ≤ 6} h x x hx hx h xfhxf. This is called the difference quotient of f, which is an important. 1. Introduction. The expression 5x − 4 > 2x + 3 looks like an equation but with e) 1+5x 2x > 5 g) 5x + 3 > 3x + 1 h) 12 − 3x 2. 2. 2 does not exist. Range: [,00) lim f(x) = 3 x lim f(x)= does not exist h→0 h. (1) (3x)³ (h) = 27x ³. (3)(3x)(4)'=27xh lim (5xx+3). R with derivative f (x)=2x since lim h→0. [(c + h)2 − c2 h. ] = lim h→0 h(2c + h) The function f: R → R defined by f(x) = |x|1/2 is differentiable.
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