Question

1. identify each relation or function as linear or nonlinear.

a. g(x)=x² + 8x + 15 a linear b nonlinear
b. 7y + 4x=-9 a linear b nonlinear
c. f(x)=1/2 a linear b nonlinear
d. h(x)=(x + 5)/4 a linear b nonlinear
e. y=-x + 12 a linear b nonlinear

1. money the table shows the amount of money remaining on a gift card each week after the gift was given.

week	0	1	2	3	4	5
amount	$100	$86	$63	$21	$9	$0

the x - intercept is __ and the y - intercept is __.

1. identify the type of symmetry for the graph of each function.

a line symmetry
b point symmetry
c no symmetry

1. for what value(s) of x are the corresponding values of f(x) relative minima?

a x=-2,1,2,4
b x = 1.5
c x=-7.5,-2.75
d x=-1,3.3

Explanation:

Step1: Recall linear - function form

A linear function has the form $y = mx + b$ or $Ax+By = C$ where $A$, $B$, and $C$ are constants and the highest power of the variables is 1.

Step2: Analyze $g(x)=x^{2}+8x + 15$

The highest - power of $x$ is 2. So it is nonlinear.

Step3: Analyze $7y + 4x=-9$

It can be rewritten as $y=-\frac{4}{7}x-\frac{9}{7}$, which is in the form $y = mx + b$. So it is linear.

Step4: Analyze $f(x)=\frac{1}{2}$

It can be written as $y=\frac{1}{2}$ or $0x + 1y=\frac{1}{2}$, which is a horizontal line (a special case of a linear function). So it is linear.

Step5: Analyze $h(x)=\frac{x + 5}{4}=\frac{1}{4}x+\frac{5}{4}$

It is in the form $y = mx + b$. So it is linear.

Step6: Analyze $y=-x + 12$

It is in the form $y = mx + b$. So it is linear.

Step7: For the $x$-intercept and $y$-intercept of the money - gift - card problem

The $x$-intercept is the value of $x$ when $y = 0$. From the table, when the amount of money ($y$) is 0, the week ($x$) is 5. The $y$-intercept is the value of $y$ when $x = 0$. From the table, when $x = 0$, the amount of money ($y$) is 100.

Step8: Analyze the symmetry of the graph in question 6

The graph has a vertical line that divides it into two mirror - image halves. So it has line symmetry.

Step9: Analyze the relative minima of the function in question 7

By observing the graph, the relative minima occur at the lowest points of the "valleys" of the graph. The $x$-values at the relative minima are $x=-1,3.3$.

Answer:

a. B. nonlinear
b. A. linear
c. A. linear
d. A. linear
e. A. linear

1. 5; 100
2. A. line symmetry
3. D. $x=-1,3.3$