a Sketch all the functions and see which of them intersects the x-axis.
B
b Sketch all the functions and see which of them intersects the x-axis
C
c Sketch all the functions and see which of them intersects the x-axis
D
d Sketch all the functions and see which of them intersects the x-axis
A
a 1
B
b 2
C
c -1
D
d 0
Practice makes perfect
a Let's draw all the functions and see which of them intersects the x-axis. We are given the function rule f(x)=3x^(â–ˇ)+1. Note that if we put -1 into the square ,we get the function f(x)=3x^(-1)+1, which can be written in the form of f(x)=3/x+1. At the same time, if we put 0 into the square we will get the constant function f(x)=1.
Out of four functions, only f(x)=3/x+1 and f(x)=3x+1 intersect the x-axis. However, we will need to use -1 later, so 1 is the answer here.
b We are given the function rule f(x)=|2x-6|-â–ˇ. Note that there is a minus sign between the absolute value and the square. Therefore, the sign of the value we pick changes to the opposite.
There are 3 functions that intersect the x-axis. However, we used 1 before and 0 will be used later on. Thus, we have to pick the value 2.
c We are given the function rule f(x)=â–ˇ x^2+1. Note that if we put 0 into the square, we will get the constant function f(x)=1.
Out of four functions, f(x)=- x^2+1 is the only one that intersects the x-axis. Therefore, -1 is the value we pick.
d We are given the function rule f(x)=â–ˇ. This means that whatever value we pick, the function is constant.
From the graph, we can see that only f(x)=0 intersects the x-axis. More specifically, the whole function lies on the x-axis. Therefore, 0 is the answer.
