Could someone tell me if I'm right, and if not what the correct answer is? Thank you! I'd appreciate an explanation, too, if you could. :)
1. Suppose you're given the following table of values for the function f(x),and you're told that the function is even:
x f(x)
-------------
–2 5
–0.35 –3
0 2
0.53 2
1 –5
Then:
f(2)= –5
f(.35) +f(–.53) = 1
***f(–1) – f(2) = –10
f(0) +f(–.53) = 0
Something is wrong. Given the table of values, the function can't be even.
2. Suppose you're given the following table of values for the function f(x), and you're told that the function is odd:
x f(x)
---------------
–2 5
–0.35 –3
0 2
0.53 2
1 –5
Then:
f(2)= 5
f(0.35) + f(–0.53) = –1
f(–1) – f(2) = –10
f(0) + f(–0.53) = 0
***Something is wrong. Given the table of values, the function can't be odd.
f(-1)=5 and f(-2)=-5 so 5--5 = 5+5= 10 that is how it is even
1. To determine if the function is even, we need to check if it satisfies the property f(x) = f(-x) for all x in its domain.
Evaluate f(2) = -5. To check if the function is even, we need to determine if f(-2) = f(2). Based on the table, f(-2) is not given, so we cannot verify this equality. Therefore, we cannot determine if f(2) = -5 satisfies the property for an even function.
Evaluate f(0.35) + f(-0.53) = 1. To check if the function is even, we need to determine if f(-0.35) + f(0.53) = 1. Based on the table, f(-0.35) and f(0.53) are not given, so we cannot verify this equality. Therefore, we cannot determine if f(0.35) + f(-0.53) = 1 satisfies the property for an even function.
Evaluate f(-1) - f(2) = -10. To check if the function is even, we need to determine if f(1) - f(2) = -10. Based on the table, f(1) is given as -5, so we can substitute the values. f(1) - f(2) = -5 - (-5) = 0. Hence, f(-1) - f(2) does not equal -10, so the function does not satisfy the property for an even function.
Evaluate f(0) + f(-0.53) = 0. To check if the function is even, we need to determine if f(0) + f(0.53) = 0. Based on the table, f(0) is given as 2, so we can substitute the values. f(0) + f(-0.53) = 2 + unknown value (since f(-0.53) is not given). Hence, we cannot determine if f(0) + f(-0.53) equals 0 for an even function.
Based on the evaluations, we can conclude that there is not enough information given in the table of values to determine if the function is even. Therefore, the statement "Something is wrong. Given the table of values, the function can't be even" is correct.
2. To determine if the function is odd, we need to check if it satisfies the property f(x) = -f(-x) for all x in its domain.
Evaluate f(2) = 5. To check if the function is odd, we need to determine if f(-2) = -f(2). Based on the table, f(-2) is not given, so we cannot verify this equality. Therefore, we cannot determine if f(2) = 5 satisfies the property for an odd function.
Evaluate f(0.35) + f(-0.53) = -1. To check if the function is odd, we need to determine if f(-0.35) + f(0.53) = -1. Based on the table, f(-0.35) and f(0.53) are not given, so we cannot verify this equality. Therefore, we cannot determine if f(0.35) + f(-0.53) = -1 satisfies the property for an odd function.
Evaluate f(-1) - f(2) = -10. To check if the function is odd, we need to determine if f(1) - f(2) = -10. Based on the table, f(1) is given as -5, so we can substitute the values. f(1) - f(2) = -5 - 5 = -10. Hence, f(-1) - f(2) equals -10, so the function satisfies the property for an odd function.
Evaluate f(0) + f(-0.53) = 0. To check if the function is odd, we need to determine if f(0) + f(0.53) = 0. Based on the table, f(0) is given as 2, so we can substitute the values. f(0) + f(-0.53) = 2 + unknown value (since f(-0.53) is not given). Hence, we cannot determine if f(0) + f(-0.53) equals 0 for an odd function.
Based on the evaluations, we can conclude that there is not enough information given in the table of values to determine if the function is odd. Therefore, the statement "Something is wrong. Given the table of values, the function can't be odd" is correct.
To determine if a function is even or odd, we need to check for symmetry in the function.
1. For the first question, we are given a table of values for the function f(x) and told that it is even. An even function is symmetric with respect to the y-axis, which means that if we reflect the graph of the function over the y-axis, it should look the same. Looking at the table of values, we can see that for each x-value, there is a corresponding y-value.
For the statement f(2) = -5, we can check if the function is even by evaluating f(-2) as well. If f(-2) = -5, then the function is even. However, f(-2) is not given in the table. Therefore, we cannot confirm or reject the statement f(2) = -5 based on the given table of values.
For the statement f(0.35) + f(-0.53) = 1, we can confirm or reject it by calculating the sum of f(0.35) and f(-0.53) based on the given table of values. Since the function is even, we can expect that f(0.35) = f(-0.35) and f(-0.53) = f(0.53). Adding these values together, we get:
f(0.35) + f(-0.53) = -3 + 2 = -1.
Therefore, the statement f(0.35) + f(-0.53) = 1 is incorrect.
For the statement f(-1) - f(2) = -10, we can check if the function is even by evaluating f(1) as well. If f(1) = -10, then the function is even. However, f(1) is not given in the table. Therefore, we cannot confirm or reject the statement f(-1) - f(2) = -10 based on the given table of values.
For the statement f(0) + f(-0.53) = 0, we can confirm or reject it by calculating the sum of f(0) and f(-0.53) based on the given table of values. Since the function is even, we can expect that f(0) = f(0) and f(-0.53) = f(0.53). Adding these values together, we get:
f(0) + f(-0.53) = 2 + 2 = 4.
Therefore, the statement f(0) + f(-0.53) = 0 is incorrect.
Based on the incorrect statements above and the given table of values, we can conclude that something is wrong. The function cannot be even.
2. For the second question, we are given a table of values for the function f(x) and told that it is odd. An odd function is symmetric with respect to the origin, which means that if we reflect the graph of the function over the origin, it should look the same. Looking at the table of values, we can see that for each x-value, there is a corresponding y-value.
For the statement f(2) = 5, we can check if the function is odd by evaluating f(-2) as well. If f(-2) = -5, then the function is odd. However, f(-2) is not given in the table. Therefore, we cannot confirm or reject the statement f(2) = 5 based on the given table of values.
For the statement f(0.35) + f(-0.53) = -1, we can confirm or reject it by calculating the sum of f(0.35) and f(-0.53) based on the given table of values. Since the function is odd, we can expect that f(0.35) = -f(-0.35) and f(-0.53) = -f(0.53). Adding these values together, we get:
f(0.35) + f(-0.53) = -3 + (-2) = -5.
Therefore, the statement f(0.35) + f(-0.53) = -1 is incorrect.
For the statement f(-1) - f(2) = -10, we can check if the function is odd by evaluating f(1) as well. If f(1) = -10, then the function is odd. However, f(1) is not given in the table. Therefore, we cannot confirm or reject the statement f(-1) - f(2) = -10 based on the given table of values.
For the statement f(0) + f(-0.53) = 0, we can confirm or reject it by calculating the sum of f(0) and f(-0.53) based on the given table of values. Since the function is odd, we can expect that f(0) = 0 and f(-0.53) = -f(0.53). Adding these values together, we get:
f(0) + f(-0.53) = 2 + (-2) = 0.
Therefore, the statement f(0) + f(-0.53) = 0 is correct.
Based on the incorrect statements above and the given table of values, we can conclude that something is wrong. The function cannot be odd.
#1
The table of values is consistent with an even function. They don't provide f(x) and f(-x) for any value of x.
Your answer is correct, because
f(-1) - f(2) = f(1)-f(-2) = -5-5 = -10
#2
The table is ok, for the same reason as given for #1.
f(0) + f(–0.53) = f(0)-f(0.53) = 2-2 = 0