Determine whether each statement is always, sometimes, or never true. an absolute value function of the form f(x)=/x+a/+b has exactly one x intercept.

Answer-

The statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

Solution-

It solely depends on b, whether the function will have one or two or zero x intercept.

This plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e V shape, with vertex translated to (-a, b), instead of origin.

1-  If b is zero, the graph will have exactly one x-intercept, at x= -a

2- If b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- If b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ The statement is sometimes true.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.