On a coordinate plane, 2 exponential fuctions are shown. Function f (x) decreases from quadrant 2 into quadrant 1 and approaches
y = 0. It crosses the y-axis at (0, 6) and goes through (1, 2). Function g (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 2) and crosses the y-axis at (0, 6).
Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?
g(x) = −6(one-third) Superscript x
g(x) = −6(one-third) Superscript negative x
g(x) = 6(3)x
g(x) = 6(3)−x
Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?
g(x) = −6(one-third) Superscript x
g(x) = −6(one-third) Superscript negative x
g(x) = 6(3)x
g(x) = 6(3)−x
2 answers:
Answer:
Step-by-step explanation:
We are provided with the information that
Function f is decreasing as it moves from quadrant 2 to quadrant 1, tending towards y=0
It intersects the y-axis at the point (0,6) and goes through (1,2).
Function g(x) also approaches y=0 in quadrant 2, but increases in quadrant 1.
It passes through (-1,2) and crosses the y-axis at (0,6).
Reflection across y-axis:
The transformation rule is identified as
Applying this rule, we derive
Then, by substituting
for x=-1
for x=0
Consequently, holds true.
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Answer:
(1, 1), (2, 2.333) and (3, 3.666).
Step-by-step explanation:
To solve this equation, we can select various values for x and then compute the corresponding y values.
<pFor instance, when x = 1, we find:4*1 - 3y = 1
3y = 3
y = 1
When x = 2, we discover:
4*2 - 3y = 1
3y = 7
y = 2.333
Then for x = 3, we have:
4*3 - 3y = 1
3y = 11
y = 3.666
Therefore, the coordinates we will plot are (1, 1), (2, 2.333), and (3, 3.666).
Refer to the attached image for the plot.
Answer:
Step-by-step explanation:
Step 1
Calculate the slope of the dashed line
The slope between two points is computed with the formula:
We consider
(-3,1) and (0,3)
and substitute into it:
Step 2
Determine the equation of the dashed line in slope-intercept form:
The equation we established is:
---> associated problem
Substituting yields:
Step 3
Establish the inequality corresponding to the graph
Given that it is represented by a dashed line, the area to the left of this line is shaded.
Thus,
Refer to the attached diagram for enhanced understanding of the problem.
Answer:
The gluten content expressed in micrograms per milliliter is 13 µg/mL.
Step-by-step explanation:
Take into account the details given.
The gluten content of the product is specified as .
We now need to convert the gluten content to micrograms per milliliter.
For conversion from mg to micrograms, refer to the following facts:
1 mg equals 1000 micrograms.
1 L corresponds to 1000 milliliters.
Next, replace 1 mg = 1000 micrograms and 1 L = 1000 milliliters into the ratio provided above.
Consequently, the gluten ratio in micrograms per milliliter is 13 µg/mL.