Choose the function to match the graph.

the graph starts at the bottom of the y axis and rises along the y axis and curves to go through the point one comma negative three and continues to the right, leveling out around y equals negative two.

f(x) = log x − 3
f(x) = log x + 3
f(x) = log (x − 3)
f(x) = log (x + 3)

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  (a)  f(x) = log x − 3

Step-by-step explanation:

The log function is zero for x=1. Here f(x) is -3 at x=1, so the log function has been shifted down 3 units.

  f(x) = log(x) -3

Here we need to remember general transformations. With that, we will see that the correct option is f(x) = log(x)− 3

Horizontal shift: For a general function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

If N is positive, the translation is to the left

If N is negative, the translation is to the right.

Vertical shift: For a general function f(x) a vertical shift of N units is written as:

g(x) = f(x) + N

If N is positive, the translation is upwards

If N is negative, the translation is downwards.

Now, we know that:

log(1) = 0

But if we look at our function, we can see that:

f(1) = -3

Then the correct option is the first one, because:

f(1) = log(1) - 3 = 0 - 3 = -3

Then we can see that this is a translation down of 3 units of the parent function log(x).

In the image below you can see the original function and the translated one:

If you want to learn more, you can read:

link

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

answer: 8

step-by-step explanation: