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Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Step-by-step explanation:

The general form of the straight line equation is, y = m·x + c

Where;

m = The slope

c = The y-intercept

The parent function is, f(x) = x

The slope of the parent function, m₁ = 1

The y-intercept of the parent function, c₁ = 0

The x-intercept of the parent function = 0

The equation of the given function g(x) is derived as follows;

Two points on the line g(x) are (-2, 5) and (1, -4)

The slope of g(x), m₂ = (-4 - 5)/(1 - (-2)) = -3

The equation of g(x) is therefore;

y - 5 = -3 × (x - (-2)) = -3·x - 6

∴ y = -3·x - 6 + 5 = -3·x - 1

y = -3·x - 1

The slope of the given function, m₂ = -3

The y-intercept of the given function, c₂ = -1

The x-intercept of the function = -1

We have that a reflection of (x, y) across the y-axis gives (-x, y)

Therefore, the function g(x) is a reflection of f(x) across the y-axis

The slope of g(x) = -3 × The slope of f(x), therefore, g(x) is obtained by a vertical stretch of of f(x) by a factor of 3

The y-intercept of g(x) is lower than the y-intercept of g(x) by -1, therefore, f(x) is shifted down vertically by 1 unit to obtain g(x)

Therefore, the sequence of transformation that can be used to obtain g(x) from the parent function f(x) are;

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

$2416.6

step-by-step explanation:

per hour = $ 25

total work time = 35

commission = 15%

total she has to make = $ 4,500

let she sold x dollar products

so her commission will be 15 % of x

now

total = weekly basic pay + commission

4500= (25*35) + 15 % of x

4500=875 + * x

4500-875 =   * x

3625= * x

multiplying wwith 100 on both sides gives

36250 = 15 x

now

x =  

x= $2416.6