Answers:
a. The domain of f is ]-∞ , ∞[
b. The range of f is [-4 , ∞[
c. f(1) = 5
d. The vales of x for which f(x) is -3 are 7 and 9
e. The points at which the graph crosses the x-axis are (6,0) and (10,0)
f. The point where the graph of f crosses the y-axis is (0,5)
g. The values of x for which f(x) < 0 are ]6 , 10[
h. f(-7) is positive
Explanation:
Part a:
The domain of the function refers to all the possible x-values that can be used as an input for this function.
Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.
In interval notation, this is written as:
Domain = ]-∞ , ∞[
Part b:
The range of the function refers to all the possible y-values that can be used as an output for the function.
From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.
This means that the range of the function starts from -4 (included) and extends to positive infinity.
In interval notation, this is written as:
R = [-4 , ∞[
Part c:
f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.
From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.
Doing this, we will find that the value of y at x=1 is 5
Therefore:
f(1) = 5
Part d:
f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3
To get the value of x, we go y=-3 and move horizontally till we intersect the graph.
Doing this, we will find that the value of y is -3 at x = 7 and x = 9
Part e:
The points where the graph crosses the x-axis are the points that have y-value equal to 0
Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)
Part f:
The point where the graph crosses the y-axis is the point that has x-value equal to 0
Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)
Part g:
f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)
Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)
In interval notation, this is written as ]6 , 10[
Part h:
f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7
From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞
This means that, at x=-7, the value of y is 5 which is a positive value
Hope this helps :)
