Question 4: The equation of g(x) is g(x) = 6x + 11
Question 3: The population of moose will be about 7692 after 12 years
Question 1: The solution of the equation is x = -11
Question 2: The solution of the inequality is any point lies in the shaded part under the dashed line
Step-by-step explanation:
Question 4:
Let us revise some transformation
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k
- A vertical stretching is the stretching of the graph away from the x-axis, If k > 1, the graph of y = k • f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k.
∵ f(x) = 2x + 5
∵ The graph of f(x) is transformed into the graph of g(x) by a
vertical stretch of 3 and a translation of 4 units down
- That means multiply f(x) by 3 and then subtract 4 from the product
∴ g(x) = 3f(x) - 4
∴ g(x) = 3(2x + 5) - 4
- Multiply the bracket by 3
∴ g(x) = 6x + 15 - 4
- Add like terms
∴ g(x) = 6x + 11
The equation of g(x) is g(x) = 6x + 11
Question 3:
The form of the exponential function is , where
- a is the initial value (value of y at x = 0)
- b is the growth/decay factor, if b > 1, then it is a growth factor, if 0 < b < 1, then it is a decay factor
∵ A moose population is growing exponentially
∵ y is the population of moose after x years
∴
- To find the values of a and b use the data in the table, x is
the first column and y is the second column
∵ At x = 0 the value of y is 40
- Substitute x by 0 and y by 40 to find a
∴
∵
∴ 40 = a
- Substitute the value of a in the equation
∴
∵ At x = 1 , the value of y is 62
- Substitute x by 1 and y by 62 to find b
∴
∴ 62 = 40 b
- Divide both sides by 40
∴ 1.55 ≅ b
∴
∴ The growth exponential equation is
- To find the population after 12 years substitute x by 12
∵
∴ y ≅ 7692
The population of moose will be about 7692 after 12 years
Question 1:
∵ 3(x + 5) = x - 7
- At first multiply the bracket by 3
∵ 3(x + 5) = 3(x) + 3(5)
∴ 3(x + 5) = 3x + 15
- Substitute 3(x + 5) by 3x + 15 in the left side of the equation
∴ 3x + 15 = x - 7
- Subtract x from both sides
∴ 2x + 15 = -7
- Subtract 15 from both sides
∴ 2x = -22
- Divide both sides by 2 to find x
∴ x = -11
The solution of the equation is x = -11
Question 2:
To draw the inequality write it as an equation y = 2/3 x + 1,
then substitute x by 0 and find y
∵ x = 0
∴ y = 2/3 (0) + 1
∴ y = 1
Plot the point (0 , 1) on the graph paper after drawing the two axes (x-axis from -7 to 7 and y-axis from -5 to 5)
Then substitute y by 0 and find x
∵ y = 0
∴ 0 = 2/3 x + 1
- Subtract 1 from both sides
∴ -1 = 2/3 x
- Divide both sides by 2/3
∴ -3/2 = x
∴ x = -1.5
Plot the point (-1.5 , 0)
Then join the two points by a dashed line
∵ The sign of the inequality is smaller than, that means shade
the part under the line
∴ The solution of the inequality is any point lies in the shaded
part under the dashed line
Look to the attached graph for more under stand
The solution of the inequality is any point lies in the shaded part under the dashed line
Learn more:
You can learn more about the equations in brainly.com/question/12967961
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