Cracking the SAT subject test in math 2, 2nd edition

Cracking the SAT Subject Test in Math 2, 2nd Edition Next, press 2ND >TRACE to access the CALC menu You can use the third and fourth options, “minimum” and “maximum”, to find local minimums and maximu[.]

Next, press 2ND->TRACE to access the CALC menu You can use the third and fourth options, “minimum” and “maximum”, to find local minimums and maximums on the graph To find a minimum, set the “left bound” to the left of a minimum, “right bound” to the right, and “guess?” close to the minimum Your calculator will find the lowest value of the function in that range Note that often you will not get an exact minimum/maximum because of the way the calculator graphs the function (by calculating a series of points)

In this case, graphing the function gives you something like this:

Because the function continues up to infinity, there is no maximum;

eliminate (D) The function also clearly goes below the x-axis; eliminate

(E) Now, you can see that you have two local minimums (to the left and

to the right of the y-axis), so you need to check both with the minimum function At both minimums, y = −7, so the range of the function is y ≥

−7, (B)

FUNCTIONS WITHIN INTERVALS: DOMAIN

MEETS RANGE

A question that introduces a function will sometimes ask about that function only within a certain interval This interval is a set of values for

the variable in the x position.

For example:

If f(x) = 4x − 5 for [0, 10], then which of the following sets

represents the range of f ?

These two questions present the same information and ask the same question The second version simply uses a different notation to describe

the interval, or domain, in which f(x) is being looked at.

Remember?

Don’t forget that x represents the independent

variable!

Be Careful

You have to be alert when domains or ranges are given in this notation, because it’s easy to mistake intervals in this form for coordinate

pairs Tricky!

The example given above also demonstrates the most common form of a function-interval question, in which you’re given a domain for the function and asked for the range Whenever the function has no exponents, finding the range is easy Just plug the upper and lower extremes of the domain into the function The results will be the upper and lower bounds of the range In the example above, the function’s

range is the set {y: −5 ≤ y ≤ 35}.

The interval that you are given means that, for that particular question, you have a different set of values for the function’s domain

DRILL 5: DOMAIN AND RANGE

Practice your domain and range techniques on the following questions The answers can be found in Part IV

9 If , then which of the following sets

(A) {x: x ≠ −2, 0, 3}

(B) {x: x ≠ 0}

(C) {x: x > −2}

(D) {x: x > 0}

(E) {x: x > 3}

15 If , then the domain of g is given

by which of the following?

(A) {x: x ≥ −2}

(B) {x: x ≠ 3, 4}

(C) {x: −2 ≤ x ≤ 6}

(D) {x: −2 < x < 6}

(E) {x: x ≤ −2 or x ≥ 6}

16 If , then which of the following sets is the

range of t ?

(A) {y: y ≠ 0}

(B) {y: y ≥ 0}

(C) {y: y ≥ 0.60}

(D) {y: y ≥ 1.67}

(E) {y: y ≥ 2.24}

19 If f(x) = 4x + 3 for −1 ≤ x ≤ 4, then which of the following gives the range of f ?

(A) {y: −4 ≤ y ≤ 7}

(B) {y: −4 ≤ y ≤ 19}

(C) {y: −1 ≤ y ≤ 7}