Question

How do the graphs of f(x) = |x| and g(x) = −2|x| compare?

Answer 1

Answer: x=|x| so gx=-2|x|

g will be -2.

g=-2

Explanation:

Answer 2

Explanation:

The graph of f(x) = |x| is a piecewise linear function with a slope of 1 for x > 0 and a slope of -1 for x < 0. The graph of g(x) = -2|x| is similar to the graph of f(x) = |x|, but it is stretched vertically by a factor of 2. This means that the graph of g(x) = -2|x| is steeper than the graph of f(x) = |x|.

The graph of f(x) = |x| is shown below:

[asy]

unitsize(1 cm);

draw((-2.5,0)--(2.5,0));

draw((0,-2.5)--(0,2.5));

label("$x$", (2.5,0), S);

label("$y$", (0,2.5), E);

draw((0,0)--(-1.5,-1.5), red);

draw((-1.5,-1.5)--(-2.5,-2.5), red);

draw((0,0)--(1.5,1.5), red);

draw((1.5,1.5)--(2.5,2.5), red);

label("$f(x) = |x|$", (2.5,2.5), NE, red);

[/asy]

The graph of g(x) = -2|x| is shown below:

[asy]

unitsize(1 cm);

draw((-2.5,0)--(2.5,0));

draw((0,-5)--(0,5));

label("$x$", (2.5,0), S);

label("$y$", (0,5), E);

draw((0,0)--(-1.5,-3), blue);

draw((-1.5,-3)--(-2.5,-5), blue);

draw((0,0)--(1.5,3), blue);

draw((1.5,3)--(2.5,5), blue);

label("$g(x) = -2|x|$", (2.5,5), NE, blue);

[/asy]