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dalvyx [7]
3 years ago
7

What transformation has changed the parent function f(x) = log5 x to its new appearance shown in the graph below? logarithmic gr

aph passing through point negative 1, negative 2.
f(x + 2) + 2
f(x + 2) − 2
f(x + 2) + 5
f(x − 2) − 5

Mathematics
2 answers:
Sloan [31]3 years ago
8 0
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.
-BARSIC- [3]3 years ago
7 0

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

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

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

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We'll start with side AC first. We can see that A is (-8, -4) and C is (-6, -2). That means to get from A to C, we need to go 2 units to the right, and 2 units up. Which means we have our two sides to work out the length from Pythagoras' theorem. 2² + 2² = c², c = √8.

Now we'll move onto side AB. We already know A is (-8, -4) from above, and B is (-7, -8). That means to get from A to B, we have to go 4 units down, and 1 unit to the right. So once again: 4² + 1² = c², c = √17.

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(I've also attached something to help you visualise how I worked it out.)

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