General Math

Question 1

When solving an equation with a square root, why must you include the plus-minus sign?

Answer 1

The square root of a number can be both positive and negative, so you must include ± to capture both solutions.

Question 2

Why is it important to only pick one value when using the square root in a function?

Answer 2

If you include both the positive and negative values, it would not pass the vertical line test, so it wouldn’t be a function.

Question 3

What’s the common mistake when factoring quadratic expressions?

Answer 3

Forgetting to check for a common factor before using other factoring methods.

Question 4

What is a common mistake when working with rational functions?

Answer 4

Forgetting to exclude values that make the denominator zero (vertical asymptotes).

Question 5

Why is it incorrect to cancel terms in a rational function before factoring?

Answer 5

Cancelling before factoring can remove terms that could reveal critical values like holes in the graph.

Question 6

Why should you be careful with the domain when dealing with logarithms?

Answer 6

Logarithms are undefined for non-positive numbers, so the domain must be restricted to positive values.

Question 7

What is the error when simplifying a power of a function inside a radical?

Answer 7

Forgetting to use absolute value when taking even roots of an expression with an even power.

Question 8

What’s a common mistake when solving exponential equations?

Answer 8

Forgetting to use logarithms to solve when the bases are different.

Question 9

Why must you be cautious with absolute value functions when solving equations?

Answer 9

You must split the equation into two cases, one where the expression inside the absolute value is positive and one where it is negative.

Question 10

What is the mistake people make with inverse functions?

Answer 10

People often forget to swap the x and y variables when solving for the inverse.

Question 11

What’s a tricky aspect of finding the inverse of a function?

Answer 11

Forgetting to restrict the domain so that the inverse is also a function (if the original function is not one-to-one).

Question 12

What do students often forget when graphing piecewise functions?

Answer 12

Forgetting to indicate whether the endpoints are open or closed based on the inequality symbols.

Question 13

Why is it important to pay attention to the horizontal asymptotes in rational functions?

Answer 13

Students often forget that the horizontal asymptote shows the end behavior but can be crossed in the middle of the graph.

Question 14

What’s a common error when working with transformations of functions?

Answer 14

Forgetting to apply horizontal stretches and compressions to the x-values rather than the y-values.

Question 15

What do students often miss when graphing transformations involving reflections?

Answer 15

Confusing the reflection across the x-axis (affects y-values) with the reflection across the y-axis (affects x-values).

Question 16

Why is solving equations with even roots tricky?

Answer 16

People often forget that taking an even root of both sides results in two possible solutions, a positive and a negative.

Question 17

What mistake is commonly made when finding the range of a function?

Answer 17

Students sometimes forget that the range is based on the y-values, not the x-values.

Question 18

What’s a tricky aspect when dealing with composite functions?

Answer 18

People often forget to check the domain of the inner function and how it affects the composite function.

Question 19

What mistake is commonly made when working with the difference of squares?

Answer 19

Students sometimes forget to use the correct pattern: (a² - b²) = (a + b)(a - b).

Question 20

What’s the common mistake when simplifying radical expressions?

Answer 20

Forgetting to rationalize the denominator by multiplying both the numerator and denominator by the conjugate.