Exam (elaborations)
MAT1510 EXAM PACK 2023
- Institution
- University Of South Africa (Unisa)
the document has the latest questions and elaborate answers
[Show more]
Content preview
MAT1510 EXAMPACK 2023
UPDATED QUESTIONS
AND ANSWERS
For inquiries and assignment help
smartwritingcompany@gmail.com
, MAT1510
PRECALCULUSMATHS1
Jan-Feb2017Solutions
QUESTION1
Givenf (x) = |1−3x|
1
andg (x) = log 1 ( 3x−2
1
) − log 3 x
3
1.1 Df andDg
Consideringf (x), thefunctionexistwhen
1 − 3x ≠0 ⇒x ≠ 31 [a function
is undefined
when divided
zero,
by so
the
denominator
in
f(x) cannot
be
zero
].
Considering g (x) ,wecanre-writethefunctionas,
g (x) = log 1 (3x − 2)−1 − log 3 x =− log 1 (3x − 2)− log 3 x .Thisfunctionvalidif
3 3
3x − 2 > 0 ⇒x > 2
3 andifx > 0 combiningthetwo,wehavex > 2
3
Df (Domainofthefunctionf(x))x : x ∈R, x ≠ 1
3
Dg (Domainofthefunctiong(x))x : x ∈R, x > 2
3
1.2 f (x) > 2
1
|1−3x| >2
If1 − 3x isgreaterthanzero,then|( 1 − 3x )|= 1 − 3x ,hence
1
1−3x >2
1 > 2 (1 − 3x)
1 > 2 − 6x
6x > 1
1
x> 6
If1 − 3x islessthanzero,then|( 1 − 3x )|= − (1 − 3x ),hence
1
−(1−3x) >2
1
3x−1 >2
1 > 2 (3x − 1)
1 > 6x − 2
, 6x < 3
1
x< 2
Solutionset:x∈R, 1
6 < x < 21 , x ≠ 1
3
1.3 g (x) > 0
1
log 1 ( 3x−2 ) − log 3 x > 0
3
Consideringthehint,weapplythechangeofbaseformula
log a
log b a = logcc b
Ingeneralthe,thelogarithmofanumbertothebaseofafractionisalwaysdifficulttodeal
with,sowechoosetochangebase31 tobase3
1
log 3 ( 3x−2 )
log 3 13
− log 3 x > 0
−log 3 (3x−2 )
−log 3 3 − log 3 x > 0
log 3 (3x − 2 ) − log 3 x > 0
log 3 ( 3x−2
x )>0
3x−2
x > 30
3x−2
x >1
3x − 2 > x
2x > 2
x>1
Solutionset:x∈R, x > 1
QUESTION2
Supposewehavetwonumbersandwhosedifferenceis8and .
2.1 Puttingtheabovestatementinamathematicalexpressionwehave,y − x = 8
Thereforey = x + 8 ,andf (x) = x + 8
2.2 S (x, y ) = x 2 + y2 ,andfromtheaboveexpressionwehave
S (x) = x2 + (x + 8)2
, S (x) = x 2 + x2 + 16x + 64
S (x) = 2x2 + 16x + 64
2.3Re-writethefunctionintheformS (x) = a(x − p)2 + q inotherwordscompletingthe
square.Inthisformthemin(ormax)valueofthefunction[turningpoint],occurswhen
independentvariable,= p .Sowehave
S (x) = 2x2 + 16x + 64
S (x) = 2[x2 + 8x + 32]
S (x) = 2[(x + 4)2 − 16 + 32]
S (x) = 2[(x + 4)2 + 16]
S (x) = 2(x + 4)2 + 32
S (x) = 2(x −− 4) 2 + 32
Sothe
x =− 4
y =− 4 + 8 = 4
QUESTION3
3.1Consideringthegiveninformationwearegiventwopointontheparabolai.e.(0,5)and
thetuningpoint(-2,9).Usingtheturningpointwehave
f (x) = a (x −− 2) 2 + 9
f (x) = a (x + 2)2 + 9
Thenusingtheotherpoint
5 = a (0 + 2)2 + 9
5 = 4a + 9
a =− 1
f (x) =− (x + 2)2 + 9
Wherea =− 1, h =− 2, andk = 9
3.2RandSareroots(x-intercepts).Theyoccurwhenf (x) = 0 ,therefore
− (x + 2)2 + 9 = 0
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller AlectaGroup. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R60,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
84866 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now