Let's find the values for each of the functions provided for the given values of $x$:

1. $f(x) = 6x^7 - 7x^5$

Evaluate this function for each value of $x = -2, -1, 0, 1, 2$:

• $x = -2$: $6(-2)^7 - 7(-2)^5 = 6(-128) - 7(-32) = -768 + 224 = -544$
• $x = -1$: $6(-1)^7 - 7(-1)^5 = 6(-1) - 7(-1) = -6 + 7 = 1$
• $x = 0$: $6(0)^7 - 7(0)^5 = 0$
• $x = 1$: $6(1)^7 - 7(1)^5 = 6(1) - 7(1) = 6 - 7 = -1$
• $x = 2$: $6(2)^7 - 7(2)^5 = 6(128) - 7(32) = 768 - 224 = 544$

2. $f(x) = \tan(x) + 4$

Make sure your calculator is in radian mode. Evaluate this function for $x = -2, -1, 0, 1, 2$ (in radians):

• $x = -2$: $\tan(-2) + 4 \approx 2.18$ (rounded to the nearest hundredth)
• $x = -1$: $\tan(-1) + 4 \approx 2.42$
• $x = 0$: $\tan(0) + 4 = 4$
• $x = 1$: $\tan(1) + 4 \approx 5.56$
• $x = 2$: $\tan(2) + 4 \approx 6.18$

3. $f(x) = \cos(x)$

Evaluate this function for $x = -2, -1, 0, 1, 2$ (in radians):

• $x = -2$: $\cos(-2) \approx -0.42$ (rounded to the nearest hundredth)
• $x = -1$: $\cos(-1) \approx 0.54$
• $x = 0$: $\cos(0) = 1$
• $x = 1$: $\cos(1) \approx 0.54$
• $x = 2$: $\cos(2) \approx -0.42$

Now, you can fill in these values into the table provided in the image.

Would you like more details on these calculations, or do you have any questions?

Related Questions

1. How do you determine if a function is odd, even, or neither based on its values?
2. Why is it necessary to use radians when working with trigonometric functions in calculus?
3. How would the values change if you used degrees instead of radians for the trigonometric functions?
4. What is the significance of symmetry in odd and even functions?
5. Can you provide examples of other polynomial functions that are either odd or even?

Tip: When using a calculator for trigonometric functions, always check that it is set to the correct mode (radian or degree) as required by the problem.