Question

# f(x) =2^{x} +1

The function *f *is defined by the equation above. Which of the following is the graph of *y = - f*(x)in the *xy*-plane?

## The correct answer is:

### Solution:-The correct option is C.

- We are given f(x) =2
^{x} +1 --------(1)

- And we have to find the graph of y = −f(x)
- From equation (1) we have to find the graph of the equation y = −(2x + 1), or y = −2x − 1.
- This should be the graph of a decreasing exponential function because as the value of x will increase value of y will decrease.
- The y-intercept of the graph can be found by substituting the value x = 0 into the equation, as follows: y = −20 − 1 = −1 − 1 = −2.

Therefore, the graph should pass through the point (0, −2).

Option C is the only function that passes through this point.

- Choices A and B are incorrect because the graphed functions are increasing instead of decreasing.
- Choice D is incorrect because the function passes through the point (0, −1) instead of (0, −2).

Therefore the correct answer is Option C

^{x}+1 --------(1)### Related Questions to study

In 1962, the population of a bird species was 2,000. The population *k *years after 1962 were 48, and *k *satisfies the equation above. Which of the following is the best interpretation of the number 61 in this

context?

**Note:**

This question could also be solved by eliminating the options. Option A is wrong as the population *k* years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population *k *years after 1962 is given by 2000-48=1952.

In 1962, the population of a bird species was 2,000. The population *k *years after 1962 were 48, and *k *satisfies the equation above. Which of the following is the best interpretation of the number 61 in this

context?

**Note:**

This question could also be solved by eliminating the options. Option A is wrong as the population *k* years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population *k *years after 1962 is given by 2000-48=1952.

### The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of *y= d(t)* on the right could represent which of the following as a function of time from when the wheel began to roll?

### The figure on the left above shows a wheel with a mark on its rim. The wheel is rolling on the ground at a constant rate along a level straight path from a starting point to an ending point. The graph of *y= d(t)* on the right could represent which of the following as a function of time from when the wheel began to roll?

### Which of the following is equivalent to ?

### Which of the following is equivalent to ?

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.

If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees.

If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)

In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

**Note: **

As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x

In the equation above, c is a constant. If the equation has infinitely many solutions, what is the value of c ?

**Note: **

As the equation is true for all values of x, we could have put x equal to any other number instead of 1, and we would get the same result. If we put x=1 in the first step as well, we would get the same value for x