1.) Describe how the graphs of f(x) = |2x| and g(x) = -|2x| are related.
a.) All of these.
b.) The graph of g(x) is a reflection of the graph of f(x) over the y-axis.
c.) Non of these.
d.) The graph of g(x) is a reflection of the graph of f(x) over the x and y axes.
e.) The graph of g(x) is a reflection of the graph of f(x) over the x-axis.
Bzzzt. E
e.) The graph of g(x) is a reflection of the graph of f(x) over the x-axis.
Just like when you try to reflect your mistakes and pretend they never happened, g(x) reflects f(x) over the x-axis. It's like looking in a mirror and realizing you've been going in the wrong direction all this time.
The correct answer is e.) The graph of g(x) is a reflection of the graph of f(x) over the x-axis.
The graph of f(x) = |2x| is a V-shaped graph that opens upwards and passes through the origin. The absolute value function ensures that the output is always positive or zero.
The graph of g(x) = -|2x| is also a V-shaped graph, but it opens downwards instead of upwards. The negative sign in front of the absolute value function reflects the graph over the x-axis, causing it to be mirrored below the x-axis.
Therefore, the graph of f(x) = |2x| and g(x) = -|2x| are related such that the graph of g(x) is a reflection of the graph of f(x) over the x-axis.
To describe how the graphs of f(x) = |2x| and g(x) = -|2x| are related, we can start by analyzing their equations.
The function f(x) = |2x| represents the absolute value of 2x. This means that for any value of x, the absolute value of 2x will be the distance of 2x from the origin on the number line.
The function g(x) = -|2x| is similar to f(x), but with a negative sign. This means that for any value of x, the negative absolute value of 2x will be the distance of 2x from the origin on the number line, but in the opposite direction.
Now, let's compare the graphs of f(x) and g(x).
The graph of f(x) = |2x| will consist of two linear segments meeting at the origin (0,0). The graph will start at (0,0) and extend upwards to the right (positive x-axis) with a slope of 2. Similarly, it will extend downwards to the right (negative x-axis) with a slope of -2.
On the other hand, the graph of g(x) = -|2x| will also consist of two linear segments meeting at the origin (0,0). However, this time the graph will start at (0,0) and extend downwards to the right (positive x-axis) with a slope of -2. Similarly, it will extend upwards to the right (negative x-axis) with a slope of 2.
Comparing the two graphs, we can see that the graph of g(x) = -|2x| is a reflection of the graph of f(x) = |2x| over the x-axis. This means that the graph of g(x) is obtained by flipping the graph of f(x) upside down.
Therefore, the correct answer is e.) The graph of g(x) is a reflection of the graph of f(x) over the x-axis.