3 Feet in a Yard.
By setting first x and then y equal to zero it is possible to find the y intercept on the
... If x = 0, then f(0) = 15 - 5(0) = 15. If y = 0, then f(x) = 0 = 15 - 5x. 5x = 15. x = 3.
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Topic 3. The definition is satisfied. The functions f and g are inverses. ... In Topic
21 we will see that the inverse of y = logbx is the exponential function y = b <sup>x</sup>.
y = f (nx), shrink horizontally by a factor of n (stretch by ) ... Stretch f vertically by a
factor of 2, and then shift f up 3 units: 2f (x) + 3 = 2(2x <sup>2</sup>) + 3 = 4x <sup>2</sup> + 3 . Shrink f ...
Only the roots, −1 and 3, are invariant. Again, Fig. 1 is y = f(x). Its reflection about
the x-axis is y = −f(x). Every y-value there is the negative of the original f(x).
Here are the graphs of y = f (x) , y = 2f (x) , and y = x . Note that if (x, y 1) is a point
on the graph of f (x) , (x, y 2) is a point on the graph of 2f (x) , and (x, y 3) is a ...
Example. f : R ! R where f(x) = x2 is not one-to-one because 3 6= 3 and yet f(3) ....
y = x + 5. Step 2. x = y 5. Step 3. f 1(y) = y 5. • Find the inverse of g(x) = 2x x1.
STEP 1: Stick a "y" in for the "f(x)" guy: y = -( 1 / 3 )x + 1. STEP 2: Switch the x and
y ( because every (x, y) has a (y, x) partner! ): x = -( 1 / 3 )y + 1. STEP 3: Solve ...
A solution of a first order differential equation is a function f(t) that makes ...
EXAMPLE 17.1.3 ˙y = t2 +1 is a first order differential equation; F(t, y, ˙y)= ˙y-t2 -1.