Step-by-step explanation:
g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.
so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.
now, we look at the graphic.
for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.
but we are looking for a c that has only one solution (one value of x to create that result).
c = 1 ?
let's imagine a horizontal line through y = 1.
we see, it cuts the function also 3 times. 3 solutions.
c = -1 ?
a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions
but c = 3 !
a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !
and that is therefore our answer.
