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Scoring notes: • A response that gives only one of x = 2 or x = 6, along with a correct justification, earns 1 of the.

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). What do ...

So if we let g(x) = 3. √x then h(x) = 3. √2x +1= g(2x + 1) = g(f(x)) . It is important to be able to decompose functions in later work in the calculus. www.

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DEFINITION OF A FUNCTION: Let X and Y two nonempty sets. ... c) h(t) is the square root of 4-3t. Only ... c) If f(x) = 2, what is x? YOU DO THIS? Example 12 on p.45 ...

First let's look at an example: EXAMPLE 3.1.2 Find the derivative of y = x−3. Using the formula, y′ = -3x−3−1 =.

The graph of the new function is easy to describe: just take every point in the graph of f(x), and move it up a distance of d. That is, if (a, b) is a point in ...

We have seen that if a parabola is in the form y = (x − h)2 + d, then we can find its vertex, its axis of symmetry, and produce a sketch with little effort.

We say that x=h x = h is a zero of multiplicity p. The graph of a polynomial function will touch the x-axis at zeros with even multiplicities. The graph will ...

To see how to calculate the volume of a general solid of revolution with a disc cross-section, using integration techniques, consider the following solid of ...