Domain: The domain for all three functions g(x), h(x), and g(x) is all real numbers since the absolute value function is defined for every real number (-∞, +∞)
Range
a) a. The range is all real numbers greater than or equal to 0,(0, +∞)
b. The range is all real numbers less than or equal to 0, (-∞, 0)
c. The range is all real numbers greater than or equal to 0, (0, +∞).
What is absolute function graph?
Given functions
a. g(x) = 5|x|
b. h(x) = -2|x|
c. g(x) = 1.5|x|
Graphs:
The graph of y = |x| is a V-shaped graph with its vertex at the origin (0,0) and extending upward and downward.
a. g(x) = 5|x| : This graph is the same as the graph of y = |x| but stretched vertically by a factor of 5.
b. h(x) = -2|x| : This graph is the same as the graph of y = |x| , but reflected across the x-axis and stretched vertically by a factor of 2.
c. g(x) = 1.5|x| : this graph is the same as the graph of y = |x| , but stretched vertically by a factor of 1.5.
Domain:
The domain for all three functions g(x), h(x), and g(x) is all real numbers since the absolute value function is defined for every real number.
Range:
a. For g(x) = 5|x|, the range is all real numbers greater than or equal to 0.
b. For h(x) = -2|x| the range is all real numbers less than or equal to 0.
c. For g(x) = 1.5|x|, the range is all real numbers greater than or equal to 0.