Question

What transformation has changed the parent function f(x) = log5 x to its new appearance shown in the graph below? logarithmic graph passing through point negative 1, negative 2.

f(x + 2) + 2
f(x + 2) − 2
f(x + 2) + 5
f(x − 2) − 5

Answer 1

F(x+2)-2 is the correct answer. I got it right on my test. Just make sure the point passing through is -1,-2 or you will miss this question. Hope I help you all.

Answer 2

Answer:

B. f(x + 2) − 2

Step-by-step explanation:

We are given the function $f(x)=\log_{5}x$.

Now, f(x) is transformed to obtain a function passing through the point (-1,-2).

So, we get that,

Translating the logarithm function by 2 units to the left and then 2 units downwards.

We get the function $f(x)=\log_{5}(x+2)-2$.

So, on substituting the value x= -1, we get,

$f(-1)=\log_{5}(-1+2)-2$

i.e. $f(-1)=\log_{5}(1)-2$

i.e. $f(-1)=-2$

Thus, the function $f(x)=\log_{5}(x+2)-2$ passes through the given point as shown below.

So, the required transformation is f(x + 2) − 2.