Which function is represented by the graph? A. f(x) = −2|x| + 1
B. f(x) = |x| + 1
C. f(x) = -2|x + 1|
D. f(x) = |x + 1|

We are given graph of an absolute function:

The standard form of an absolute function is :

y=a| x−h |+k, where (h,k) is the vertex of the graph.

For the given graph of absolute function, we have vertex at (0,1).

And because it's open down the value of a should be a negative number.

|a| >1, it would vertically stretch by a factor of 2.

Therefore, correct option is first option.

f(x)=-2|x| + 1.

Step-by-step explanation:

A

Step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.