All categories

3 years ago

Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|

Mathematics

2 answers:

Vika [28.1K]3 years ago

7 0

Answer: h(x) = |x+10|

---------------------------------------------------------

Explanation:

To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).

So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|

We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.

prisoha [69]3 years ago

4 0

To move a graph c units to the right, minus c from every x
to move a graph c units to the left, add c to every x

g(x)=|x|
move to left 10 units
add 10 to every x
h(x)=|x+10| is the equation of g(x) translated 10 units to the left

You might be interested in

What is the equation of a line that goes through the point (0,2) and has a slope of -1 ?

OLEGan [10]

Answer: <u><em>A, because when x=1/-1 you don't need to write down the one meaning it is -x and then +2 is the y which means the full answer is y=-x+2</em></u>

8 0

3 years ago

One side if the labtop is 9.5 inches and the other side is 14 inches. Using the Pythagorean Theron, what is the length of the di

Digiron [165]

(side 1)² + (side 2)² = (diagonal)²

(9.5² + (14)² = (diagonal)²

90.25 + 196 = (diagonal)²

286.25 = (diagonal)²

√286.25 = √(diagonal)²

17 = diagonal

Answer: 17 inches

3 0

3 years ago

You buy 1.75 pounds of apples and 2.05 pounds of oranges. Apples and oranges sell for the same price per pound. The total cost,

dlinn [17]

Answer:

$1.75c+2.05c=4.18\\\\Per\ pound\ cost=c=\$1.1$

Step-by-step explanation:

$Cost\ of\ per\ pound\ apple=Cost\ of\ per\ pound\ oranger=c\\\\$

Cost of Apples:

$Amount\ of\ apples=1.75\ pounds\\\\Cost\ of\ apples=Amount\times per\ pound\ cost\\\\Cost\ of\ apples=1.75\times c\\\\Cost\ of\ apples=1.75c$

Cost of oranges:

$Amount\ of\ oranges=2.05\ pounds\\\\Cost\ of\ oranges=Amount\times per\ pound\ cost\\\\Cost\ of\ oranges=2.05\times c\\\\Cost\ of\ oranges=2.05c$

Total cost:

$Total\ cost\ of\ fruits=cost\ of\ apple+cost\ of\ oranges\\\\Total\ cost\ of\ fruits=1.75c+2.05c\\\\After\ coupon\ cost=\$ 3.43\\\\ Original\ cost=After\ coupon\ cost+coupon\ amount\\\\ Original\ cost=3.43+0.75=4.18$

$1.75c+2.05c=4.18\\\\3.8c=4.18\\\\c=\frac{4.18}{3.8}\\\\c=1.1\\\\Per\ pound\ cost\ of\ fruits=\$1.1$

4 0

3 years ago

Which exponential function is represented by the graph?

Anna [14]

Answer:

Step-by-step explanation:

Let's solve this using our formula for exponential functions:

$y=a(b)^x$ where a is the initial value and b is the growth/decay rate. We will fill that equation in with 2 of the coordinates on the graph and come up with the values for both a and b. (0, 3) and (1, 6):