Day 45 of 60 · Fri 13 Nov · Daily workbook · CAT in 16 days

Day 45: Functions & Graphs + Arrangements Set + Science RC

Day 45 of the free ThinkCAT 60-day CAT challenge: 5 functions & graphs questions and 3 spaced-review QA questions, a full arrangements DILR set (4 questions), a science RC passage (4 questions), plus para jumbles and odd one out. Every question is a real CAT PYQ.

QA · 8
DILR · 4
VARC · 6
40 minutes
Real CAT questions

Concept card

Functions & Graphs

Core formulas

Domain: no zero denominators, no negatives under even roots, log arguments > 0
f(g(x)): apply g first
Even: f(−x) = f(x). Odd: f(−x) = −f(x)
f(x − a) moves right by a; f(x) + b moves up by b; f(|x|) mirrors the right half

60-second shortcut · Functional equations

Try x = 0, 1 and −1 first. For f(x) + k·f(1/x) = g(x), replace x by 1/x and solve the pair.

Trap box

Looks like: f(g(x)) = g(f(x))Actually: Order matters: apply g first
Looks like: Range = the values you can plug inActually: That is the domain; range is what comes out

From the free Algebra Formula Sheet (PDF).

What's in Day 45

QA: Functions & Graphs (5) + 3 spaced-review questions
DILR: Arrangements set, 4 questions
RC: Science passage
VA: Para Jumbles, Odd One Out

Year, slot and question number for each question appear with the answer key after you submit.

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