{"id":167,"date":"2014-11-19T21:13:44","date_gmt":"2014-11-19T21:13:44","guid":{"rendered":"https:\/\/purple-mathbelt.marjoriesayer.com\/?page_id=167"},"modified":"2020-11-21T20:04:48","modified_gmt":"2020-11-21T20:04:48","slug":"week-5-transformations-day-1","status":"publish","type":"page","link":"https:\/\/purple-mathbelt.marjoriesayer.com\/?page_id=167","title":{"rendered":"Week 5: Transformations – Answers"},"content":{"rendered":"

Week 5: Transformations – Day 5
\n<\/strong>
\nEach function g(x) below is a transformation of a basic function f(x). Say what f(x) is, and describe the transformation (sometimes there is more than one transformation). For extra practice graph both g and f on the same set of axes.<\/p>\n

1. g(x) = (x – 5)2<\/sup><\/p>\n

f(x) = x2<\/sup> and the transformation is a horizontal shift 5 units to the right.<\/p>\n

2. g(x) = -|x| + 1<\/p>\n

f(x) = |x| and there are two transformations: reflection in the x-axis and a vertical shift up 1 unit.<\/p>\n

3. g(x) = sqrt(-x) (square root of -x)<\/p>\n

f(x) = sqrt(x) and the transformation is reflection in the y-axis.<\/p>\n

4. g(x) = 3(x + 1) – 4<\/p>\n

There is some leeway here about what is f(x). If you say:
\nf(x) = 3x – 4 ( a line of slope 3 passing through (0, 4)) then the transformation is a simple horizontal shift 1 unit to the left.<\/p>\n

If you say f(x) = 3x, there are two transformations: vertical shift down by 4 units, horizontal shift left by 1 unit.<\/p>\n

If you say f(x) = x, there are three transformations: vertical shift down by 4 units, horizontal shift left by 1 unit, and a vertical stretch by 3 units.<\/p>\n

5. g(x) = – (x + 1)<\/p>\n

f(x) = x and there are two transformations: horizontal shift left by 1 unit and reflection in the x-axis.<\/p>\n

\n

 <\/p>\n

Week 5: Transformations – Day 4
\n<\/strong>
\nIf f(x) is a function, the function g(x) = f(-x) is the reflection of f in the y-axis. In all of the problems below, g(x) = f(-x).<\/p>\n

1. If f(x) = x – 1, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.<\/p>\n

g(x) = -x – 1<\/p>\n

\"sketch1\"<\/a><\/p>\n

2.\u00a0If f(x) = |x – 1|, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.<\/p>\n

g(x) = |-x – 1| = |x + 1|<\/p>\n

\"sketch2\"<\/a><\/p>\n

3.\u00a0If f(x) = x2<\/sup> + 1, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.<\/p>\n

g(x) = (-x)2<\/sup> + 1 = x2<\/sup> + 1 = f(x)<\/p>\n

This is an example of an even function<\/strong>, where f(x) = f(-x), and its graph is symmetric about the y-axis.<\/p>\n

\"sketch3\"<\/a><\/p>\n

4. If f(x) = -(x – 1)2<\/sup>, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.<\/p>\n

g(x) = -(-x – 1)2<\/sup> = -(x + 1)2<\/sup><\/p>\n

\"sketch4\"<\/a><\/p>\n

5. If f(x) = |x + 2|, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.<\/p>\n

g(x) = |-x + 2| = |2 – x| = |x – 2|<\/p>\n

\"sketch5\"<\/a><\/p>\n

\n

 <\/p>\n

Week 5: Transformations – Day 3
\n<\/strong>
\nWhat is the formula of the function with the given horizontal shift?<\/p>\n

1. The function g(x) is obtained from f(x) = |x| by shifting to the right 5 units.<\/p>\n

What is the formula for g(x)?<\/p>\n

g(x) = |x – 5|<\/p>\n

2. g(x) is obtained from f(x) = x3<\/sup> by shifting to the left 1 unit.<\/p>\n

What is the formula for g(x)?<\/p>\n

g(x) = (x + 1)3<\/sup><\/p>\n

3. g(x) is obtained from f(x) = x2<\/sup> – 7x + 1 by shifting to the right 3 units.<\/p>\n

What is the formula for g(x)?<\/p>\n

g(x) = (x – 3)2<\/sup><\/p>\n

4. g(x) is obtained from f(x) = (x – 10)4<\/sup> + 9 by shifting to the left 2 units.<\/p>\n

What is the formula for g(x)?<\/p>\n

g(x) = (x + 2 – 10)4<\/sup> + 9
\ng(x) = (x – 8)4<\/sup> + 9<\/p>\n

5. g(x) is obtained from f(x) = |x – 3| + x by shifting to the right by 1 unit.<\/p>\n

What is the formula for g(x)?<\/p>\n

g(x) = |x – 1 – 3| + (x – 1) = |x – 4| + x – 1<\/p>\n

\n

 <\/p>\n

Week 5: Transformations – Day 2<\/strong><\/p>\n

Rewrite the following functions with the indicated shift.
\nThe transformed function will be called g(x).<\/p>\n

1. Shift up 2 units: f(x) = 2x – 4<\/p>\n

The transformed function is g(x) = 2x – 4 + 2 = 2x – 2<\/p>\n

2. Shift down 3 units: f(x) = 4x3<\/sup><\/p>\n

g(x) = 4x3<\/sup> – 3<\/p>\n

3. Shift up 10 units: f(x) = sqrt(x) (f(x) = square root of x).<\/p>\n

g(x) = sqrt(x) + 10<\/p>\n

4. Shift up 5 units: f(x) = 1\/x<\/p>\n

g(x) = 1\/x + 10 = (1 + 10x) \/ x<\/p>\n

5. Shift down 100 units: f(x) = x1.5<\/sup><\/p>\n

g(x) = x1.5<\/sup> – 100<\/p>\n

\n

 <\/p>\n

Week 5: Transformations – Day 1<\/strong><\/p>\n

1.<\/p>\n

\"longrectangle2\"<\/a><\/p>\n

2.<\/p>\n

\"longrectangle2\"<\/a>\"longrectangle2\"<\/a>\"isosceles2-2\"<\/a><\/p>\n

3.<\/p>\n

\"isosceles-tilt2\"<\/a><\/p>\n

4.<\/p>\n

\"pentagon-2\"<\/a><\/p>\n

5.<\/p>\n

\"diamond2-1\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Week 5: Transformations – Day 5 Each function g(x) below is a transformation of a basic function f(x). Say what f(x) is, and describe the transformation (sometimes there is more than one transformation). For extra practice graph both g and f on the same set of axes. 1. g(x) = (x – 5)2 f(x) = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":13,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-167","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/167","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=167"}],"version-history":[{"count":9,"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/167\/revisions"}],"predecessor-version":[{"id":202,"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/167\/revisions\/202"}],"up":[{"embeddable":true,"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/pages\/13"}],"wp:attachment":[{"href":"https:\/\/purple-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}