Question

Identify the function that contains the data in the following table:

x     -2         0         2         3         5    
f(x)     5         3         1         2         4    
a. f(x) = |x| + 1
b. f(x) = |x - 2|
c. f(x) = |x - 2| - 1
d. f(x) = |x - 2| + 1

Answer 1

Answer:

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

Step-by-step explanation:

put the value of x in the functions and check the results

Answer 2

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

Step-by-step explanation:

From the given values of f(x) corresponding to the values of x, we take only one pair of values, say (0,3).

Now, we have to check which equation from the given four satisfies the ordered pair (0,3).

Here, the first function is f(x) = |x| + 1, where putting x = 0, we get f(x) = 1 ≠ 3.

And, the second function is f(x) = |x - 2|, where putting x = 0, we get f(x) = 2 ≠ 3.

And, the third function is f(x) = |x - 2| - 1, where putting x = 0, we get f(x) = 1 ≠ 3.

Finally, the fourth function is f(x) = |x - 2| + 1, where putting x = 0, we get f(x) = 3.

Therefore, the fourth function f(x) = |x - 2| + 1 is the required function. (Answer)