Which function has a range of {y|y ≤ 5}?

f(x) = (x – 4)2 + 5
f(x) = –(x – 4)2 + 5
f(x) = (x – 5)2 + 4
f(x) = –(x – 5)2 + 4

The correct option is 2.

Step-by-step explanation:

The range of a parabola is {y|y ≤ 5}.

It means the maximum value of the function is 5. It is possible if the vertex of a downward parabola is in the form of (h,5).

The vertex form of a parabola is

Where, (h,k) is vertex and a is a constant.

If a<0, then f(x) is a down ward parabola and if a>0, then f(x) is an upward parabola.

In option 1,

It is an upward parabola with vertex (4,5), therefore the range of the function is {y|y ≥ 5}. Option 1 is incorrect.

In option 2,

It is a downward parabola with vertex (4,5), therefore the range of the function is {y|y ≤ 5}. Option 2 is correct.

In option 3,

It is an upward parabola with vertex (5,4), therefore the range of the function is {y|y ≥ 4}. Option 3 is incorrect.

In option 4,

It is a downward parabola with vertex (5,4), therefore the range of the function is {y|y ≤ 4}. Option 4 is incorrect.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.