hi! number one and number two are causing me trouble, so if anyone would like to answer either that’d be appreciated. thanks in advance:)

Step-by-step explanation:

1a) The function will shift 5 units to the right, 4 units down,

1b).The function will shift 3 units to the left, stretched in the y direction by a scale factor of 3, and shift up 2 units.

2a). The function will shift 2 units to the left, reflect over the x axis, and shift 2 units down.

2b) The function will stretched in the y direction by a scale factor of -2 and shift the function up 3 units.

9514 1404 393

  1a. translation right 5, down 4

  1b. vertical stretch ×3, translation left 3, up 2

  2a. translation left 2, down 2

  2b. reflect in x, vertical stretch ×2, translation up 3

  3. f(x) = -4/(x+5)+4

  4. f(x) = 1/2√(3(x +3)) -4

Step-by-step explanation:

Transformations of functions can be decoded by considering the transformation ...

  g(x) = a·f((x-h)/b) +k

The transformations here are ...

Note that either 'a' or 'b' can be a fraction less than 1, which results in a transformation usually described as a compression (not a stretch). If either of these is negative, then a reflection over the x-axis (a<0) or y-axis (b<0) is also involved. The stretch (or compression) and/or reflection is applied before the translation the way this is written.

_____

1a. translation right 5, down 4

1b. vertical stretch by a factor of 3, translation left 3, up 2

__

2a. translation left 2, down 2

2b. reflected across the x-axis, vertically stretched by a factor of 2, translated up 3

__

3. a=4, b=-1, h=-5, k=4

f(x) = -4/(x+5)+4

__

4. a=1/2, b=1/3, h=-3, k=-4

f(x) = 1/2√(3(x +3)) -4

_____

The graphs in the attachments show the various functions. (It takes a little work to verify that the graph in the last attachment has the appropriate compressions, but it does.)

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.