Transformations by hand

Medium0 of 10 parts

Ten short questions on moving and stretching graphs. Where a rule is asked for, give it in terms of $x$ ; abs(x) is how you type $|x|$ , and sqrt(x) is how you type a square root.

Remember the two habits: anything outside the function acts vertically and as written, and anything inside acts horizontally and backwards, after the inside has been factored into the form $b(x - h)$ .

Write the rule for $y = |x|$ moved 4 to the left and 2 down.

in terms of x

Write the rule for $y = x^2$ stretched vertically by a factor of 3 and then reflected in the x-axis.

in terms of x

The graph of $y = -2(x + 1)^2 + 5$ has a turning point. Give its x-coordinate.

For the same graph, $y = -2(x + 1)^2 + 5$ , give the y-coordinate of the turning point.

Write $y = (2x - 6)^2$ in the form $y = \bigl(2(x - h)\bigr)^2$ and give $h$ .

$f$ is odd and $f(3) = 7$ . Find $f(-3)$ .

$f$ is even and $f(-5) = 2$ . Find $f(5)$ .

With $f(x) = |x|$ , write the rule for $y = f(2x)$ in terms of $x$ .

in terms of x

A V-shaped graph has its corner at $(3, -1)$ and passes through $(5, 3)$ . In the form $y = a|x - 3| - 1$ , find $a$ .

With $f(x) = x^2$ , write the rule for $g(x) = f(x - 3) + 4$ in terms of $x$ .

in terms of x