Match the following functions
a) f (x) = 2 to the power of x +1
b) f (x) = 3x -2
c) f (x) = (x + 1) to the second power
d) f(x) = vertical line x + 1 vertical line
e) f(x) = square x to the 3rd power
f) f (x) = x(2x +5)
g) f(x) = fraction x over 2
h) f (x) = fraction 8 over vertical line x vertical line + 3
with the correct values below:
1. f(5) = 36
2. f(5) = 64
3. f(-7) =6
4. f(-1) = 2
5. f(2) = 4
6. f(2) = 18
7. f(8) = 2
8. f(8) = 4
a) f(x) = 2 to the power of x + 1 => 2. f(5) = 64 => 2. f(2) = 18
b) f(x) = 3x - 2 => 6. f(-7) = 6 => 5. f(2) = 4
c) f(x) = (x + 1) to the second power => 3. f(-1) = 2
d) f(x) = |x + 1| => 4. f(-1) = 2
e) f(x) = x^3 => Not matched
f) f(x) = x(2x + 5) => Not matched
g) f(x) = x/2 => 7. f(8) = 2
h) f(x) = 8/|x| + 3 => 1. f(5) = 36 => 8. f(8) = 4
Matching the functions with the correct values:
a) f(x) = 2^x + 1
1. f(5) = 36 (Correct)
b) f(x) = 3x - 2
6. f(2) = 18 (Incorrect)
c) f(x) = (x + 1)^2
5. f(2) = 4 (Correct)
d) f(x) = |x + 1|
3. f(-7) = 6 (Incorrect)
e) f(x) = x^3
2. f(5) = 64 (Incorrect)
f) f(x) = x(2x + 5)
Not matching any values.
g) f(x) = x/2
Not matching any values.
h) f(x) = 8/(|x| + 3)
4. f(-1) = 2 (Correct)
7. f(8) = 2 (Incorrect)
Correct matches:
1. a)
2. c)
4. h)
To match the given functions with the correct values, we need to substitute the given values of "x" into each function and determine which function produces the given output.
a) f(x) = 2^(x+1)
Substituting x = 5 into this function:
f(5) = 2^(5+1)
= 2^6
= 64
Therefore, function "a" matches with value #2.
b) f(x) = 3x - 2
Substituting x = 5 into this function:
f(5) = 3(5) - 2
= 15 - 2
= 13
None of the given values match 13, so function "b" does not match any of the given values.
c) f(x) = (x+1)^2
Substituting x = -7 into this function:
f(-7) = (-7 + 1)^2
= (-6)^2
= 36
Therefore, function "c" matches with value #1.
d) f(x) = |x+1|
The vertical line notation represents the absolute value function.
Substituting x = -1 into this function:
f(-1) = |-1 + 1|
= |0|
= 0
None of the given values match 0, so function "d" does not match any of the given values.
e) f(x) = x^3
Substituting x = 2 into this function:
f(2) = 2^3
= 8
None of the given values match 8, so function "e" does not match any of the given values.
f) f(x) = x(2x + 5)
Substituting x = 2 into this function:
f(2) = 2(2(2) + 5)
= 2(4 + 5)
= 2(9)
= 18
Therefore, function "f" matches with value #6.
g) f(x) = x/2
Substituting x = 8 into this function:
f(8) = 8/2
= 4
Therefore, function "g" matches with value #8.
h) f(x) = 8/|x| + 3
Substituting x = 8 into this function:
f(8) = 8/|8| + 3
= 8/8 + 3
= 1 + 3
= 4
Therefore, function "h" matches with value #7.
Matched functions with correct values:
a) f(x) = 2^(x+1) matches with value #2.
c) f(x) = (x+1)^2 matches with value #1.
f) f(x) = x(2x + 5) matches with value #6.
g) f(x) = x/2 matches with value #8.
h) f(x) = 8/|x| + 3 matches with value #7.