Let h(x)=2x+4. If g(x) is a vertical stretch of 3 units and a horizontal translation 6 units left, what is the rule for g(x)?
in Algebra 1 Answers by Level 1 User (220 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

My guess is that, if h(x)=2x+4, g(x)=3(2(x+6)+4)=6(x+6)+12=6x+36+12=6x+48.

The effect is to shift the straight line 2x+4 6 units to the left, which means it intersects the x axis at -8 instead of -2; and the line is steeper, so the slope increase from 2 to 6, a factor of 3. This is a stretch in the vertical direction of 3.

by Top Rated User (1.1m points)
Rudolf decides to make and sell necklaces to earn money to buy a new computer. He plans to charge $4.75 per necklace.

a) Write a function that describes the revenue R(n), in dollars, Rudolf will earn from selling n necklaces.

b) What is a reasonable domain for this function?

c) Graph the function.

d) Identify and interpret the intercepts of the function.

a) R(n)=4.75n

b) Perhaps Rudolf can make 100 necklaces to buy a computer costing $475, so the domain would be 1 to 100 or perhaps 0 to 100 if he couldn't be bothered to make even one!

c) Straight line passing through the origin with a slope of 4.75.

d) The intercepts are both 0.

Use the two given functions to choose the best statement comparing the graphs to each other.
Function 1: y=-x-3    Funtion 2: y=x+1
A. Function 2's graph is shifted down 4 units from Function 1's graph and is reflected.
B. Function 2's graph is shifted down 4 units from Function 1's graph and is not reflected.
C. Function 2's graph is shifted up 4 units from Function 1's graph and is reflected.
D. Function 2's graph is shifted up 4 units from Function 1's graph and is not reflected.

Red line is Function 1, blue line is Function 2.

When x=0 (y axis) the lines are separated by 4 units with 1 sitting below 2, so Function 2 is shifted up from Function 1. The two functions are reflections of one another if by reflection is meant that, for example, (-1,0) is a reflection of (-3,0) and (-1,-2) reflects (-3,-2) where the vertical line x=-2 is a double-sided mirror.

So, Function 2's graph is shifted up 4 units from Function 1's and is not reflected, correct?
Not sure about the reflection part because I don't know how reflection is defined.
Use the two given functions to choose the best statement comparing the graphs to each other.

Function 1: y=-x+3       Function 2: 2x+1

A. Function 2's graph is less steep than Function 1's graph and is reflected.

B. Function 2's graph is steeper than Function 1's graph and is reflected.

C. Function 2's graph is less steep than Function 1's graph and is not reflected.

D. Function 2's graph is steeper than Function 1's graph and is not reflected.

Your original commented question:

Did some checking. Reflection seems to be defined two ways for functions.

If F1(x)=F2(-x) or F1(x)=-F2(x) then F1 reflects F2 in one or other axis.

Clearly this is not the case for Functions 1 and 2, so you're right, under this definition Function does not reflect Function 2. Everything depends on how reflection is defined.

Now let's see your new question.

I think the answer is D. The coefficient 2 makes Function 2 steeper. By the above definition of reflection, the functions do not reflect each other.

Related questions

1 answer
asked Jul 3, 2022 by anonymous | 330 views
1 answer
asked Apr 14, 2022 by August | 259 views
1 answer
asked Jul 6, 2020 by anonymous | 1.1k views
1 answer
asked Mar 4, 2019 in Word Problem Answers by anonymous | 144 views
2 answers
asked Nov 9, 2016 in Other Math Topics by anonymous | 3.3k views
1 answer
asked Jul 11, 2016 in Other Math Topics by anonymous | 496 views
1 answer
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,939 users