Answer:
- domain: -∞ < x < ∞
- range: -∞ < y ≤ -1
- f(-5) = -2
- f(-1) = -4
Step-by-step explanation:
Function values and the extent of the graph can be determined by reading the graph.
<h3>Domain</h3>
The domain of the function is the set of values for which the function is defined. It is the horizontal extent of the graph. The graph shows the function is defined for all real numbers.
The domain is -∞ < x < ∞.
<h3>Range</h3>
The range of the function is the set of output values the function may have. It is the vertical extent of the graph. The graph shows the function can have any value no greater than -1.
The range is -∞ < y ≤ -1.
<h3>Function values</h3>
Function values can be read from the graph by locating the x-value on the x-axis, and following the vertical line to its intersection with the function graph. The y-value of that point is the function value.
f(-5) = -2
f(-1) = -4
Or, we can write the function definition based on the graph, and use that definition to find the values at specific points. The graph is of the absolute value function reflected over x and translated <-4, -1>.
f(x) = -|x+4| -1
f(-5) = -|-5 +4| -1 = -1 -1 = -2
f(-1) = -|-1 +4| -1 = -3 -1 = -4
and 
may be linearly dependent, so that their span forms a subspace of 
that does not contain every vector in 
and 
. Any vector 
of the form 
, where 
, is impossible to obtain as a linear combination of these 
and 
.